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American Economic Association

Unemployment, Inflation, and MonetarismAuthor(s): Jerome L. SteinReviewed work(s):Source: The American Economic Review, Vol. 64, No. 6 (Dec., 1974), pp. 867-887Published by: American Economic AssociationStable URL: http://www.jstor.org/stable/1815239 .

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Unemployment,nflat ion,a n d Monetarism

By JEROME L. STEIN*Edmund Phelps criticized the game planof the Council of Economic Advisers onthe grounds that they had no explicitmodel of the U.S. economy to justify thepolicies that were undertaken to curb theinflation.

The Council's Report provides a lookat the 1969-71 game plan to disinflateby means of retarding aggregate de-mand.... The President-Elect's TaskForce on Inflation recommended, as afirst interim step, that aggregate de-mand be slowed so as to bring the un-employment rate back to some equilib-rium region around 4.5 percent....What happened was that, under thecover of the expectation and acceptanceof such a limited step towards re-equi-libration, the Administration graduallytightened monetary and fiscal policy soseverely as 'gradually' to send the un-employment rate whizzing past theequilibrium zone to around 6 percent.To my knowledge the theory of how,and how well, this medicine would act tocure the patient of his inflation wasnever spelled out by the Council of Eco-nomicAdvisers.[pp.533--34]

Since the Council had no explicit model ofthe U.S. economy, they could neither ex-plain the paradox of unemployment cuminflation nor could they evaluate the prob-able effects of alternate economic policies.The econometrics of wage and price de-termination have been actively studied inreceint years. Important articles on this

subject appear in the Brookings Papers onEconomic Activity and in the Proceedingsof the Federal Reserve-Social Science Re-search Council (SSRC) Conference (editedby Otto Eckstein, papers by Hymans,Klein, de Menil and Enzler, Hirsch, Bod-kin, Ball and Duffy, Eckstein and Wyss,Heien and Popkin, and Andersen andCarlson, among others). The Proceedingswere analyzed by James Tobin in hissummary comments. These studies gen-erally contain three equations: a wagechange equation, a price change equation,and an equation describing the formationof price expectations. The unemploymentrate is taken as an exogenous variable; andthe models do not explicitly containmonetary and fiscal policy variables.'Therefore, they cannot explain (i) thesimultaneous determination of, and inter-actions between, the unemployment andinflation rates and (ii) the effects of mone-tary and fiscal policies upon the paths ofthe unemployment and inflation rates.The Andersen and Carlson study is anexception, however; it does contain theunemployment rate as an endogenous vari-able as well as the monetary and fiscalpolicy variables. It can and has been usedto simulate the effects of policy. However,that model cannot be solved analytically;and its theoretical foundations are neitherclear nor widely accepted.2

* Brown University. I am indebted to W. Bomberger,G. H. Borts, M. Friedman, J. Frenkel, H. Hori, E. F.Infante, N. Liviatan, and J. P. LaSalle for their per-ceptive criticisms of an earlier draft. The John SimonGuggenheim Foundation provided financial assistancefor this study, which was written while I was at theHebrew University in Jerusalem.

1 Tobin summarized the FRB-SSRC models in thisway: "These four equations form a subsystem of a com-plete model that given an initial price history is capableof determining prices, price expectations, and wages.Unemployment, past and present, and rental cost ofcapital can be taken as exogenous to the subsystem"(1972a, p. 6).2 Two studies of the relation between unemployment

867

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868 THE AMERICANECONOMIC REVIEW DECEMBER 1974Paul Samuelson wrote that "The centralissue that is debated these days in connec-tion with macro-economics is the doctrine

of monetarism" (p. 7). However, there isno satisfactory theory of monetarism.Milton Friedman's attempt to provide atheoretical explanation of the monetaristposition has been deemed unsuccessfulboth by neo-Keynesians and by otherleading monetarists. Tobin describedFriedman's theoretical framework as fol-lows:He undoubtedly hoped that the use of acommon theoretical apparatus wouldreduce the controversy about the rolesof monetary and fiscal policies to aneconometric debate about empiricalmagnitudes. If the monetarists and theneo-Keynesians could agree as to whichvalues of which parameters in whichbehavior relations imply which policyconclusions, then they could concentrateon the evidence regarding the values ofthose parameters. I wish that thesearticles had brought us closer to thisgoal, but I am afraid they have not.

[1972c, pp. 852-53]According to Karl Brunner, who is a lead-ing exponent of monetarism:Monetarist ideas have become almostrespectable in recent years and the cen-tral propositions about the role of moneyand monetary policy have been increas-inglv accepted or at least seriously pon-dered. Still, the monetarist position re-mains an unsettled issue with respect toboth its degree of confirmation and itsanalytic formulation. [p. 2]

Brunner and Allan Meltzer agree withTobin's criticism of Friedman's article onmonetarism: "We regard Friedman's dis-cussion as either misleading or a completereversal of his often stated position" (p.846).My paper attempts to explain the phe-nomena of unemployment cum inflationand the analytic foundations of the mone-

tarist position within the context of asingle model.In Section I, I develop a simple small-scale dynamic model of the economy,whose salient features are accepted bymost macro-economic theorists. The statevariables are denoted by X, and it is thevector containing the unemployment rate,the rate of price change, and the expectedrate of price change. Control variablesdenoted by vector C are the monetary andfiscal policies followed by the government.The dynamic model described by

DX= AX+ BC, D _ dldtis easily solved analytically because itonly contains three linear differentialequations with constant coefficients. Everyequation can be understood very easily,and the dynamics of the system and ef-fects of policies can be clearly traced. Itssteady-state and dynamic properties arediscussed in Section II. Section III ex-plains the phenomenon of unemploymentcum inflation, and Section IV explains thelogical foundations of monetarism, on thebasis of the model contained in Sections Iand II. A simple phase diagram is used asa graphic device to explain the qualitativeimplications of the dynamical system.Quantitative accuracy can only be ob-tained by estimating the coefficients of thedynamic model. Preliminary work alongthis line is encouraging, but is not reportedhere. My exclusive concentration in thispaper is upon the theory.

I. A Simple Dynamic Model ofthe MacroeconomyIn the short run, the ratio of effectivelabor supplied per unit of capital is as-sumed to be relatively constant; and thestate variables are the unemployment rate(U), the rate of price change (ir), andthe expected rate of price change (wx*).This section develops the complete model

applicable to an economy where the ratioand inflation must also be mentioned: David Laidlerand the paper by the author and Ettore Infante.


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VOL. 64 NO. 6 STEIN: MONETARISM 869of effective labor supplied per unit of cap-ital is also a state variable. In the subse-quent parts, only the short-run versionwill be used.

A. The Labor Market and theUnemployment Equation

The Walrasian labor market adjustmentequation (1) states that the rate at whichnominal wage W changes is a linear com-bination of two elements: the expectedrate of price change ir*, and the state ofthe labor market.

DW lNd - NDW~ ~~XXI2(Va ) > 0No dichotomy is made between expecta-tions of employers and of employees in thissingle sector macro-economic model; hence7r*reflects both the expected change in theprice of output and the expected change inthe price of goods purchased by consumers.The state of the labor market is reflectedby the second term X1(.). Variables Ndand Ns refer to the quantities of labor ser-vices demanded and supplied, respectively.Function X' is positive; the growth of thenominal wage DW/W is positively relatedto the excess demand forlabor(Nd-N,)/N,for the usual reasons.If the state of the labor market is given,variations in the expected rate of pricechange by employers and employees leadimmediately to corresponding changes inthe growth of the nominal wage.Assume that technical change is Harrod-neutral, so that "effective labor" is a mul-tiple A (t) of labor in natural units. Thenequation (1) can be written as (2) whereXd and x, refer to effective labor per unit ofcapital demanded and supplied, respec-tively. Ratio Nd/N, = Xd/X, when technicalchange is labor-augmenting.(2) DW = 7r* + (Xd -Xs)w x8

Uf

\Ut

0 Xd x

FIGURE 1. THE UNEMPLOYMENT RATE IS NEGATIVELYRELATED TO THE EXCESS DEMAND FOR LABOR

The excess demand for labor is not di-rectly observable, though the closest di-rect measure of it may be the number ofvacancies less the number of people unem-ployed. Equation (3) states that the mea-sured unemployment rate U is negativelyrelated to the excess demand for labor; andit is described in Figure 1. This assump-tion permits both positive and negativeexcess demands for labor to be associatedwith a positive unemployment rate. Itdoes not require that we assume that thequantity of labor employed is the smallerof the quantity demanded or supplied.At full employment (see Figure 1), theunemployment Uf Ns is equal to vacan-cies. Equation (3) is sufficiently general tobe consistent with a wide range of micro-economic theories of labor markets. Theinverse function is described by equation(4).

/Xd - Xs\(3) HH' < 0; 1 _ U _ 0

(4) H-1(U) = __ (HK1)'< 0Xs

The actual ratio of effective labor em-


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870 THE AMERICAN ECONOMIC REVIEW DECEMBER 1974ployed per unit of capital, denoted by x(without a subscript), is equation (5)below.3(5) x-(1 - U)x"If equation (4) is substituted into (2),then the frequently used wage changeequation (6) is derived. Function h is thecomposition of X1and H-1, i.e., h-=1 o H-1,and h' is negative. Equation (7) is a linear-ization of (6).

DW(6) - 7r*+h(U), h' < OwDW(7) = 7r* + ho- hlUw

The excess demand for labor per unit ofcapital (equation (8) below) requires someexplanation. The demand for labor arisesfrom the private and the governmentsectors. In the private sector, the quantityof labor demanded per unit of capital de-pends upon the real wage w adjusted forthe level of technology A(t). Specifically,the quantity of labor demanded by theprivate sector per unit of capital dependsupon w/A (t). Some of the output will bepurchased by the private sector and somewill be purchased by the government. Thegovernment also purchases the services oflabor directly: the real gross productoriginating in the government sector is thereal value of the compensation of em-ployees. It is identically equal to a fixedmultiple of the labor input of governmentemployees, because gross product in con-stant prices per man-hour in the govern-ment sector is defined (by the Department

of Commerce) to be unchanging over time.The government is not a profit maximizerin the conventional sense. Its direct de-mand for labor services per unit of capitalG, can be taken as a control variable dif-fering in magnitude from its purchases ofgoods from the private sector. Assume forsimplicity that GC s a fraction t of totalreal government purchases of goods andservices per unit of capital G; i.e., G1= G.In general, t will not be a constant, andboth t and G will constitute control vari-ables. Therefore, the quantity of labordemanded per unit of capital4 dependsupon w/A (t) and {G, and is xd= F(w/A (t),G)The supply of effective labor per unit ofcapital x, is assumed to be inelastic withrespect to the real wage, and in the "shortrun," ratio x, is assumed to be relativelyconstant. Therefore, the excess demand forlabor per unit of capital, resulting fromthe activities of the private sector, is re-lated to w/A(t) the adjusted real wage.Combining the private and governmentsectors equation (8) is derived.

Xd - X(8) - =1 ,(j YG; xX, t ifl < O, f2 > ?Substitute equation (4) into (8) and de-rive equation (9). This shows the depen-dence of the unemployment rate U on theadjusted real wage w/A (t) and on the realvalue of government purchases of goods

3The implication of (3) and (5) is that the ratio ofemployment to the quantity demanded N/Nd = X/Xd isI - H (- _ Ix Xs

Xd Xd/X,At any instant of time, firmsare not necessarily on theirdemand curves for labor nor are households necessarilyon their supply curves.

4Let xl be the quantity of labor demanded per unitof capital in the private sector which produces goodspurchased by both the private sector and the govern-ment. Then w/A (t) = F*(x') or xl = F(w/A (t)), where Fis the inverse of F*, is the labor demand function. Thegovernment, which is not a profit maximizer in the usualsense, demands x" of labor per unit of capital in theeconomy. Then Xd=X+X,' = F(w/A (t))+x1'. Since GIis defined as xl', then Xd = F(w/A (t)) + G1. It is assumedthat all of the capital is in the sector producing goods.If G1 {G, where G is the total demand by the govern-ment for goods and services per unit of capital, then,Xd = F(wlA (t))+FG.


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VOL. 64 NO. 6 STEIN: MONETARISM 871* wA(t) G

G1U~~~~w2

WO B AUt Ue

h U)a

DW_ 'FIGURE 2. THE DETERMINATION OF THE EQUILIBRIUM

UNEMPLOYMENT RATE Ue AND ADJUSTEDREAL WAGE W*

and services per unit of capital.5/w \(9j H-1(U) =f t( Y G)

This basic equation is illustrated in the tophalf of Figure 2. The unemployment rateis positively related to the trend adjustedreal wage w/A(t), and negatively relatedto the government's direct demand forlabor services.Differentiate equation (9) with respectto time and derive equation (10). Althoughthe coefficients ,1 and O2 are functions oftime, I treat them as relatively constantvalues in order to work with a time invari-ant linear system. Coefficient ,1 is an elas-ticity.

Dw\(10) DU= K a)- 2DGwwhereB1=-f1(H-1)wlA > 0 02=--f2/- (H-1)'

> 0 and DA /A = a. Substitute (6) into(10), since DW/W-7r = Dw/w, and derivedifferential equation (11) for the change inthe unemployment rate. If the linear formof the wage change equation (7) were used,then differential equation (12) would bederived.(11) DU = ,01(7r* h(U) -7r - a)- ,2DG

=-lh(U) - 01w + ilr*- a41- ,2DG

(12) DU= 1(7r*+1hoh1iU - r-a)- ,2DG

= (-3lhl) U-lr +17+ *+ Oi(ho - a) - ,2DG

These formulations imply Friedman's"natural" (equilibrium) rate of unemploy-ment Ue because the coefficient of 7r*in equation (1) is unity. When the actualrate of price change is fully anticipated,and both U and G are constant, then (12)implies (13).(13) Ue = (ho - a)jhlEquations (12) and (13) are macro-economic relations which reflect the dis-tribution of employment and unemploy-ment among various sectors, each of whichmay have a different relation between theunemployment rate and the correspondingrate of nominal wage change. The disper-sion of the unemployment may be reflectedby ho and h1, and the equilibrium rate ofprice change may affect the dispersion ofunemployment and employment. There-fore, the equilibrium rate of price changemay affect the equilibrium unemploymentrate via vector (ho, hi, a) even though thecoefficient of 7r in equation (1) is unity. Itwould be surprising if the macro-economicequilibrium rate of unemployment Uewere constant over a decade, since the dis-tribution of employment and unemploy-ment are unlikely to be constant. This isan empirical question to be examined. In-

I Since x, is considered to be relatively constant, itwill not be written explicitly in the f( ) function.


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872 THE AMERICANECONOMIC REVIEW DECEMBER 1974telligent economic policy must take intoaccount the likelihood that (ho, h,, ca)maynot be constant over time, and may evenbe related to the equilibrium rate of pricechange.6Define x1- U- Ue, the deviation of theunemployment rate from the equilibriumrate Ue. Then Dxl=DU. Substitute (13)into (12) and derive equation (14), thedifferential equation for the unemploy-ment rate.(14) Dxi =_ lhl xl -7r + Olr* - DGThis equation states that the change in thedeviation x1 between the actual and theequilibrium unemployment rate is nega-tively related to the deviation xi, nega-tively related to unanticipated inflation(7r-7r*), and negatively related to thechange in real purchases of goods andservices by the government. Variable DGis a control variable, variables 7r and 7r*are state variables which I shall now dis-cuss.

B. Price Change EquationsA virtue of the widely used adaptiveexpectations equation (15) is that expecta-tions are allowed to change slowly butsmoothly in light of past experience. If thereader were asked to predict the rate ofinflation over the coming year, the ex-pected rate of monetary expansion wouldbe an important variable in determininghis forecast; and he would not confine his

attention to a weighted average of pastrates of price change. Further work mustbe directed to replacing this equation withsomething better.7 In the interim, I use(15) to reflect expectations which may bechanging slowly.(15) Dir* = b(r - *)

where (wr--*) is unanticipated inflation ordeflation.8The actual rate of price change r is theresultant of excess demand and cost pres-sures. If there were no excess demand forgoods and services, the rate of price changewould equal the growth of the nominalwage DW/IW less the trend rate of tech-nical progress a. There seems to be a con-sensus that this is a measure of cost pres-sure.9 If (DW/W-a) were zero, then therate of price change would be proportionalto E, the excess demand for goods per unitof capital. Coefficient X, is a finite speedof response.10(16) r = DW/W-a +XpEMy discussion of the determinants of theexcess demand for goods per unit of capital

6 This issue has been discussed by Tobin (1972a, b)and in the Brookings Papers in connection with thesubject: Has the Phillips curve shifted?7See Tobin (1972a) and the author, pp. 64-66.

8There are two extreme cases of equation (15). In(a), the expected rate of price change is equal to thecurrent rate; in effect b is infinite.(a) 7r* =7XAlternatively, b is zero, and the expected rate of pricechange is equal to the long-run steady-state value 7r,.We know that 7re is equal to the rate of monetary ex-pansion , less the long-run growth of effective labor n.(b) W*=7re =,U-n

9The price change equation used in much of the re-cent econometric literature (see Tobin (1972a)) is:DW7r = a12 W - aI3a + aI47r* + f(U - Ue)w

where U, is the average or normal unemployment rate.In these empirical studies the unemployment rate istaken as exogenous. The main findings are that a12-a13= 1, and a modest effect of demand pressure is esti-mated, where U- U is negatively related to demandpressure.10I could have used the price change equation whichcharacterized the "synthesis" model of money andgrowth (see the author, ch. 5): 7r= 7r*-+X,E where 7* isthe expected rate of price change. The rationale behindthis equation is that specialists change prices on thebasis of expectations 7r*and market conditions E. Equa-tion (16) in the text above implies that

lr = r* +J (U) -a + XE = 7r* + (E, U,a)which is formally similar to the price change equationin the synthesis model. See the author and Infante,pp. 539-41.


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VOL. 64 NO. 6 STEIN: MONETARISM 873will be terse, since it is largely based uponmy 1971 study.

C. The Excess Demand for GoodsThe excess demand for goods per unit ofcapital E is equal to planned investmentper unit of capital I/K plus planned con-sumption per unit of capital C/K plus realgovernment purchases per unit of capitalG less output per unit of capital Y/K.Define planned savings as output lessplanned consumption. It follows thatI S

(1~~' E =- K+ GK Kis the real excess demand for goods perunit of capital."Investment decisions are made byfirms, and are independent of the savingsdecisions of households. The followingmodel of the investment process was de-rived from Keynes' analysis in the Trea-tise, I, pp. 200-09. The desired change inthe ratio of capital to output is positivelyrelated to the demand price of capitalrelative to its supply price. The supplyprice is just the price of a unit of currentoutput P(0). The demand price (capitalvalue) is equal to the present value of theexpected rents. Therefore, the desiredchange in the ratio of capital to output ispositively related to the ratio of the pres-ent value of quasi rents to the price of aunit of current output. Let R(t) be theexpected marginal physical product of theunit of capital at time t; P*(t) the ex-pected price of output at time t; P(0) thecurrent price of output; 5 the depreciationrate; and p the expected constant nominalrate of interest equal to the current rate.Then the ratio of the demand price ofcapital to its supply price is given by (18).

demand price of capital(18) C=q- supply pricer R(t) P*(t)| -~~~e-PtdtP(0)

Assume that: (i) the price of output is ex-pected to change at proportionate rate 7r*such that P*(t) = P(O)e-*t, and (ii) themarginal physical product of capitalR(t) = re-It, where r is the current mar-ginal physical product of capital. Equation(18) can be written as (19) when the de-nominator is positive; i.e., when the nom-inal rate of interest p exceeds the expectedappreciation 7r*- 3 of the asset.(19) q = rf exp [-(p + 6 - r*)t]dt

rp+6 -

The desired change in the capital-outputratio is assumed to be positively related to(q- 1), the gap between the demand priceof capital and its supply price. Whenq>1 or r+7r*-5>p, then firms wish toraise the ratio of capital to output. Whenq

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874 THE AMERICANECONOMIC REVIEW DECEMBER 1974proportion. Speed of response g is assumedto be finite.12Output per unit of capital y dependsupon the ratio of effective labor per unitof capital x, as described by equation (21).(21) y =y(x); y' >O, y"

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VOL. 64 NO. 6 STEIN: MONETARISM 875interest p; and (iii) real balances per unit ofcapital m. The first variable is an oppor-tunity cost for owners of wealth, so thatthe excess demanded is negatively relatedto R(U)+7r*. For the usual reasons, thenet excess demand for bonds by the privatesector is positively related to the nominalrate of interest p. Real balances and realbonds are complementary assets in port-folios, so that the quantity of real bondsdemanded per unit of capital should bepositively related to real balances per unitof capital. Moreover, the quantity of realbonds supplied per unit of capital shouldbe negatively related to the stocks of realbalances per unit of capital held by firms.The real private excess demand for bondsper unit of capital can be written asB(R(U)+7r*, p, m), where B10,B3>0.Let z be the real stock of governmentinterest-bearing debt per unit of capital.Then equilibrium in the bond marketimplies that:(29) B(R(U) + lr*,p, m) = z

Equation (30) describes the nominalrate of interest which equilibrates the bondmarket, and the partial derivatives havethe usual signs.(30) p = p(U,r, mn,z)where pi= -B1R'jB20;p3==-B3/B20. Since z ispositively related to Om (real privatewealth per unit of capital), the interestrate equation can also be written as (31)where gi and pi have the same signs. Theimportant point is that, given m, a risein 0 (or z) raises the nominal rate of interestby shifting the traditional LM curve up-wards.Walras' law for stocks implies that,since the bond market is in equilibrium,the excess demand for real balances isequal to the excess supply of real capital.

(31) p = g(U, 7r*, m, 0);gl < O, g2 > O, g3 < 0, g4 > 0

Substitute (31) into (28) and deriveequation (32) for the excess demand forgoods per unit of capital when the bondmarket is in equilibrium.(32) E = E(U, 7r*, m, G, 6; x.)Function E does not contain p, the nomi-nal rate of interest, as an argument. Thesign of aE/lO is the subject of controversy.A rise in 0, given m, will shift the LM curveupwards and raise the nominal rate ofinterest. Private investment will therebybe inhibited. On the other hand, the risein 0 may raise consumption demand (viaequation (26)), and thereby shift the IScurve upwards. The net effect of a rise in 0upon E is not obvious on a priori grounds;and it is at the heart of the monetaristcontroversy.

D. The Differential Equation for theRate of Price ChangeThe actual rate of price change is de-rived by substituting (32) and (7) into(16), and equation (33) is obtained.

(33) X .= * + ho-h U- a+ XpE(U, 7r*,m, G, 6; x,)

= P(U, 7r*,m, G, 0; x;)where

O7w/OU=Pi=- h+XPE,o7r/(97r*=P2= 1+XPE2m(3r/dim) = P3 = mXpE3cw/oG= P4= XpE4Ow06= P5= XPE5

Note that the unemployment rate U, andthe expected rate of price change 7r*, af-fect both the costs of producing outputand the excess demand for goods per unitof capital. This equation differs from theprice adjustment equations commonlyused in empirical work primarily because


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876 THE AMERICAN ECONOMIC REVIEW DECEMBER 1974state variable m and control variables Gand 0 explicitly appear. Note also that P3is an elasticity, for a reason that will beapparent shortly.The proportionate rate of change of realbalances per unit of capital is given byequation (34).

Dm DK(34) = _m Kwhere ,u is DM/M the rate of monetaryexpansion and DKIK is the growth ofcapital. Since x,-=AN8 K is assumed to berelatively constant in the short run andeffective labor AN, grows at rate n, equa-tion (35) can be used in place of (34).

Dm(35) - = ,u-7r-nmThe current rate of price change ir in equa-tion (33) depends upon m, which is theintegral of past policies.

rtm(t) = m(O) expf ( r) 7r(T) - n)dr

For this reason the economic system re-sponds slowly to current monetary policydescribed by A(T)), n contrast to the mod-els where consumption depends upon dis-posable income. Differentiate (33) withrespect to time, and derive equation (36):Dm(36) Dir = PjDU + P2Dir* + P3 m

+ P4DG + P5DOSubstitute (35), (15), and (14) into (36)and derive differential equation (37).When the long-run (or full) system is con-sidered, then (34) rather than (35) will besubstituted into (36); and DKIK willreplace n.(37) Dir =-P1/1h1x1+ (P2b-P131-P3)r

+ (P131 - P2b) ir*+ (P4 - P1,32)DG+ P3(, -n)+P5DO

The construction of the dynamical sys-tem, where the ratio of effective labor perunit of capital is relatively constant, isnow complete. The model contains threedifferential equations in three state vari-ables: U, wr,and -x*. The long-run systemis obtained by relaxing the assumptionthat x, is relatively constant.13

II. The Short-Run Dynamical Systemand its Equilibrium PropertiesThere are three state variables in theabove short-run macro-economic model:the deviation x= U- Ue of the unemploy-

ment rate from its equilibrium level; therate of price change 7r; and the expectedrate of price change 7r*. Control variablesare: the change in real government pur-chases of goods and services14 per unit ofcapital DG; the rate of monetary expan-sion per unit of effective labor g-n; andopen-market operations and debt manage-ment policies of the treasury DO. Equa-tion (38) describes the dynamic model interms of a vector-matrix differential equa-tion whose components are equations (14),(15), and (37). Let vector X=(x1, r, 7r*)and C=(DG, ,.-n, DO). Then equation(38) can be written compactly as (39).A flow chart (Figure 3) is helpful invisualizing this system of differential13 An easy way to do it is to assume that effectivelabor supplied grows exogenously at rate n. Then

(a) Dx,/x, = it - DK/KOutside the steady state, planned savings need notequal planned investment. Assume that the growth ofcapital is a linear combination of planned savings andplanned investment, as described by equation (b).(b) DKIK = aI/K + (1 -a)S/K, 1 > a > OThe complete model can now be reduced to four differ-ential equations in four state variables: U, 7r, 7r*,and x,;and the phenomena of unemployment and price changesare viewed in the context of a growing economy. Seethe author, Keizo Nagatani, and H. Rose.

14 There is really another instrument that has beensuppressed for the sake of simplicity: the distribution ofgovernment purchases between goods and direct laborservices, ratio G1/G. The taxes less transfer paymentsare implicit in the model via the government budgetconstraint.


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VOL. 64 NO. 6 STEIN: MONETARISM 877FEEDBACK

expected rate of

zo o B '9 0:C COST PUSHx nominal' _

uSti wageKA

D -rate ofprice waeal K,change balances >i1~~~~~~~zH ~~~~~~~H

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878 THE AMERICAN ECONOMIC REVIEW DECEMBER 1974equations. Wage change equation (6) isdescribed by link B (price expectationterm) and link H (the unemployment rate).Price change equation (33) is the sum ofthe cost push link C and demand pull linkL. The adaptive expectations equation islink A. Price change expectations operateon prices directly through links B and C,and indirectly through link D, the excessdemand for goods. The unemploymentequation consists of links F and the left-hand side of link I.Two policy inputs are depicted in theflow chart. Real government purchases ofservices operate directly upon the unem-ployment rate via the left-hand side of I;and real government purchases of goodsoperate upon the excess demand for goods,the right-hand side of link I. The secondpolicy input is the rate of monetary expan-sion, link J. Changes in the rate of mone-tary expansion operate on money balances,and the excess demand for goods is affectedvia link K. Monetary policy can affect theunemployment rate indirectly by changingthe real wage through link E. The cir-cuitous route connecting monetary policyto the unemployment rate runs from J toK to E to F.

A. Characteristics of the Steady StateDefine the steady state as a situationwhere the state variables X are constant(DX=O) and control variables DG andDOare zero. It is not assumed that A-n iszero. What are the characteristics of thesteady state? Let subscript e denotesteady-state values. Figure 2 is helpful inunderstanding the nature of the steadystate. When the expected and actual ratesof price change are equal, then (6) or (7)states that the growth of the real wage

(DW/W-7r)e is negatively related to theunemployment rate; and it is described bythe curve in the lower part of Figure 2.When the unemployment rate U and realgovernment purchases per unit of capitalare constant, then according to (10), the

real wage will rise at the trend rate ofgrowth of productivity a. Only at unem-ployment rate Ue will the growth of thereal wage (DW/W-Fr)e be equal to a.That is:(40) (DW/W - 7r)= a = h(Ue)Therefore, the equilibrium unemploymentrate Ue depends upon the h function andthe rate of technical progress a: the higherthe rate of technical progress, the lowerwill be the equilibrium rate of unemploy-ment.The upper part of Figure 2 is based uponequation (9). It states that the unemploy-ment rate is positively related to the ad-justed real wage w* = wIA (t) and nega-tively related to the level of G. If therewere a rise in G from G1 to G2, then thelevel of unemployment corresponding tow* would decline from Ue to U'. Howeverthe real wage would rise at a faster ratethan a if the level of unemployment fellbelow Ue. The rise in the real wage wouldlead to a decline in employment in theprivate sector; and the unemploymentrate would rise above U'. Equilibriumwould prevail when the real wage rose tow* (point C). The transfer of labor to thelabor-intensive G sector would raise thereal wage, but no change would occur inthe unemployment. The equilibrium ad-justed wage w*= wIA (t) is given by equa-tion (41). It is a function of Ue and G.

(41) H- (Ue) =f(w* G) = H-[h-l(a)]Two other important results occur in thesteady state. There will be a zero excess de-man for goods per unit of capital. This canbe seen from (16), repeated here.

(16) r = DWIW-a- +XpEWhen the real wage grows at a, then(42) E(U, 7r*,m; G, 0, x,) = 0The market for goods will be in equilib-rium.


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VOL. 64 NO. 6 STEIN: MONETARISM 879Finally, the equilibrium rate of pricechanlge 7rewill be such that real balancesper unit of capital will be constant. This

follows from equation (36) or (37) whenxl=w7r-7r*=DG=D6=O. Then 3 (- n-7)=0. Since P3 is not zero,(43) 7e =u- nThe rate of price change is equal to therate of monetary expansion less the growthof effective labor.The excess demand for goods must bezero when the steady state is attained.Therefore,E(Ue, 7e, mte; G, 0, x8)

= E(Ue, A - n, me; G, 0, x8) = 0Solve this equation for me and obtain theequilibrium level of real balances per unitof capital. In this manner, the entire sys-tem is solved for its steady-state proper-ties.Assume that: (a) the Routh-Hurwitzconditions for dynamic stability are satis-fied, and (b) each element along the prin-cipal diagonal of matrix A is negative.The second assumption states that if(n- 1) state variables are fixed at theirequilibrium values, deviations of the nthvariable from its equilibrium value will beeliminated asymptotically. The secondassumption is convenient, but not neces-sary, for the subsequent dynamic analysis.

III. Unemployment and InflationA. A nalytical Techniques

A graphic explanation of the unemploy-ment cum inflation phenomenon can bepresented through the use of phase dia-grams, which are based upon vector-matrix differential equation (38).Write the first equation in (38) as:(44) Dxl = (-31jh)x1 - f13r + f17r* - 02DGWhen 7r-7r*=DG=O, then xi will con-verge asymptotically to zero; the unem-

ployment rate will converge to the equi-librium Ue as described in (13). It is con-venient, but not necessary, to assume thatthere is an equilibrium rate of unemploy-ment which is independent of the rate ofprice change; i.e., that (ho, hi, a) in equa-tion (13) are quite stable and are not sig-nificantly affected by macro-economicmonetary and fiscal policy.We know (Section IIA above) that7* =,= u=-n in the steady state. To de-scribe (38) in two dimensions so that aphase diagram can be used, it is useful todefine a new variable z: the difference be-tween the equilibrium rate of price change7e=A-n and current expectations. In thesteady state, z will be zero.(45) z = (,u-n)-r* or r* = u-n-zSubstitute (45) into the first equation of(38) and obtain (46).(46) Dxi = (-Olhl) -Xi - 17-r + 31(&L - n)

- 1lZ - f2DGDefine the EE' curve as the set of (xi,r) along which Dx1= O. It is equation (47)below.

(47) 7r =-hlxl + (,-u-n-z)- - DGCThis curve is negatively sloped. Why? Ifxi rises, the rate of growth of the nominalwage declines by h1Ax1units. If the rate ofprice change declined by the same amount,the adjusted real wage (w/A(t)) wouldbe constant; and hence the unemploymentrate would not change. For this reason theEE' curve is negatively sloped.Deviations of x1 from the EE' curve,given 7r, tend to be eliminated because itwas assumed that each element along theprincipal diagonal of (38) is negative, i.e.,it was assumed that

(Dxl(48) ox, = -lh < 0Ox1 7


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880 THE AMERICAN ECONOMIC REVIEW DECEMBER 1974The horizontal vectors in Figure 4 de-scribe this phenomenon. What is happen-ing in economic terms? If unemploymentrate deviation xl is to the right of the EE'curve, the proportionate rate of change ofthe nominal wage will decline by hi units.Thereby, the growth of the adjusted realwage will decline by hi units. For everypercentage point decline in the adjustedreal wage, the employment rate will rise by/1 units (equation (10)). It follows thatdeviations of the unemployment rate fromequilibrium tend to be eliminated, giventhe values of the other state variables.Disequilibrium in the labor market (xi #0)will produce repercussions upon the com-modity market which, in turn, will affectthe rate of price change; and thereby thelabor market will be disturbed. Some ofthese effects will now be discussed.Write the second equation in (38):

Dir = (-31h1P1)x1 + (P2b - Pfl3 - P3)w? (Pil3 - P2b)r*+ [(-P4 P1f2) DG + P5 DO]+ P3( -n)

Substitute 7r* ,-n-z into the aboveequation and derive:(49) Dr = (-O1ihP1)x1

? (P2b - P1t1 - P3)w? (Pl?l + P3-P2b)(,u-n)- (Plil - P2b)z + P5DO+ (P4 - P1g2)DG

Define the PP' curve as the set of (xi, 7r)such that Dr= 0. It is described by equa-tion (50) and is drawn in Figure 4.-/hk1P1(50) ir =- -x(P3 + P131 - P2b)

+ [(P4 - P112)DG + P5DO - (Pl, - P2b)z](P3 + P131 - P2b)

The dynamic system is assumed to be

stable; and the elements along the prin-cipal diagonal of matrix A are assumed tobe negative such that inequality (51) issatisfied.

&Dir(51) - = -(PI01 + P3-P2b) < O9r xIThe vertical vectors in Figure 4 describethis phenomenon. Given x1, deviations in7r tend to be eliminated. A unit rise in wrabove the PP' curve induces three distinctforces: some tend to produce further de-viations of 7r,and others tend to restore itto its equilibrium value. These basic forcesare reflected by P13l, P3, and P2b and aredescribed graphically in the flow chart(Figure 3).(a) First: A rise in 7r raises the ex-pected rate of price change by b units.Two subeffects are produced: one in thelabor market and the other in the com-modity market. The rise in the expectedrate of price change raises the growth ofthe nominal wage; and the latter raisescosts. Moreover, the rise in the expectedrate of price change raises planned invest-ment because the real rate of interest tendsto decline relative to the rent per unit ofcapital. The increase in the excess demandfor goods exacerbates the rate of inflation.As a result of a unit deviation of the rateof price change from equilibrium, the ex-pected rate of price change rises by bunits;and the rate of inflation is raised bybP2= b(1+X,E2) units. This is an elementof instability.(b) Second: A rise in 7r ends to lowerthe growth of the adjusted real wage; andunemployment tends to decline by /1 units.Several countervailing effects, summarizedby -O3P1i=(iz(h1-X,Ei), are produced:(i) The growth of the nominal wage is in-creased by /1h1 units and the resulting risein costs is passed on in the form of a higherrate of price change. Inflation is aggra-vated. (ii) The decline in unemploymentincreases output; and both savings and


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VOL. 64 NO. 6 STEIN: MONETARISM 88177'

ElE2sPi~ ~ ~ ~ ~~~i

Eo\~~~~~~~~~~~~E 2

FIGURE 4. THE STEADY DECLINE IN G(DGO, andthat the full Routh-Hurwitz conditionsfor stability are satisfied.If the system is to be dynamicallystable, then it is necessary that the slopeof the PP' curve be algebraically greaterthan that of the EE' curve. The slope ofthe PP' curve will depend upon the sign of-Pi=hf-XPE,, an effect which was dis-cussed above. In Figure 4, the PP' curveis drawn with a negative slope;15 but the

15 Preliminary empirical work suggests that the PP'curve is negatively sloped and that the system is dy-


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882 THE AMERICAN ECONOMIC REVIEW DECEMBER 1974analysis would be similar if it were posi-tively sloped.

B. The Phenomenon ExplainedIt is convenient for graphic exposition(but not necessary for an algebraic an-alysis) to make a monetarist assump-tion (to be discussed in Section IV below)that [(P4-P1i2)DG+P5D0], in equation(50) describing the PP' curve, is approxi-mately zero. Moreover, assume that the nu-merator of the coefficient of z (Plfl -P2b) /(P3+P101-P2b) is sufficiently small asto be ignored.16 Then the EE' and PP'curves can be described by equations (52)and (53), respectively.(52) wr=-hixi+ [(,-n-z)--DG](53) r=1- _ SU-nP3When Mo-n=z=DG=0, the EE' curvewill be described by EoEo and the PP'curve will be described by P0P' in Figure4. The resulting equilibrium (xi, r)= (0, 0)is stable.Suppose that real government pur-chases of goods and services per unit ofcapital were declining (DG

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VOL. 64 NO. 6 STEIN: MONETARISM 883time (say, a year) if it is subject to thecustomary shocks and disturbances of apeacetime economy" (Patinkin, p. 901).

Clearly, a graphic description of a thirdorder (3x3) system can only sketch itsbasic features. However, this model hasbeen shown to be capable of explainingthe qualitative features of the unemploy-ment cum inflation paradox.IV. The Monetarist Controversy

The dynamic model developed abovecan also explain the issues involved in themonetarist controversy. Thereby, the con-troversy about the roles of monetary andfiscal policies can be reduced to an econo-metric debate about empirical magnitudes.The crucial propositions held by sophis-ticated monetarists can be briefly stated.Mi. "Changes in the pace of economicactivity are not associated with anyparticular monetary growth and occurindependently of the level of monetary

growth. They only depend on the previ-ous changes in monetary growth, what-ever its inherited level" (Brunner, pp.14-15).M2. "The impact of monetary accelera-tions (or decelerations) on output andemployment is essentially temporary"(Brunner, p. 13).M3. "Monetary growth affects domi-nantly the price level" (Brunner, p. 13).M4. "The slope of the LM curve is not thekey difference between the monetaristsand the neo-Keynesians" (Friedman,p. 910).M5. "To have a significant impact on theeconomy, a tax increase must somehowaffect monetary policy-the quantityof money and its rate of growth.Whether deficits produce inflation de-pends on how they are financed. If, as sooften happens, they are financed bycreating money, they unquestionablydo produce inflationary pressure. If they

are financed by borrowing from the pub-lic, at whatever interest rates are neces-sary, they may still exert some minorinflationary pressure. However, theirmajor effect will be to make interestrates higher than they would otherwisebe" (Friedman, p. 915).M6. "Government spending unaccompa-nied by accommodative monetary ex-pansion, that is financed by taxes orborrowing from the public, results in acrowding out of private expenditureswith little, if any, net increase in totalspending" (Andersen and Carlson, p. 8).The monetarists could accept the dif-ferential equation for the unemploymentrate:Dxl = (-Olhl)xl - /13 + lwr* - f2DG

If the government does not hire labor di-rectly, but just purchases goods from theprivate sector, then G1=O. This is theusual case considered by the monetarists;however, I wish to consider the generalcase where the government purchases bothgoods and services.The monetarists make the following as-sumptions:(a) There is an equilibrium rate ofunemployment which is independent ofthe rate of price change. It is their conten-tion that (ho kil,a) in equation (13) aboveare quite stable, and are not significantlyaffected by macro-economic policy. Thisassumption is'necessary to derive mone-tarist conclusions. The EE' curve is equa-tion (47), repeated here.(47) =r -h1x1

+ [(u - s z) - DG]aDxl(48) -lh, < Oax1

(b) The expected rate of price changetends to adjust to the current rate with a


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884 THE AMERICAN ECONOMIC REVIEW DECEMBER 1974lag. Otherwise, monetary policy would notbe able to exert even a temporary effectupon the unemployment rate. That is, if7r*(t) = 7r(t) for all t, and DG(t) =0, thenxl(t) will converge asymptotically tozero, 17 regardless of the rate of pricechange or the nature of current monetarypolicy.(c) concerns the PP' curve. In gen-eral, the PP' curve is equation (50) re-peated here.(50) -1i x (A-n(P3+P1,i1-P2b)

+ [(P4-P1p2) DG+P5D0](P3+P101-P2b)

(Pjl3 - P2b)z(P3+P1,1-P2b)

dD7r(51) - - (P101+P3-P2b)

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VOL. 64 NO. 6 STEIN: MONETARISM 885(c) Quantity [(P4-P1/2)DG+P5DG] isapproximately equal to zero so thatgovernment expenditures financed

through the sale of debt do not exerta perceptible effect upon excess ag-gregate demand.A diagrammatic explanation of themonetarist conclusions (M1-M4) can alsobe given on the basis of the above modelsummarized by equations (47), (48), (55),and (51).Suppose that ,-n=DG=z=O. Thenthe EE' and PP' curves are described bythe EEo and PoP' curves, respectively, inFigure 5. Both curves intersect at thesteady-state solution, which is the originin this case. The system is assumed to be

stable. Directions of motion are describedby the horizontal and vertical vectors;and the economy will converge to thesteadystate x1=0, 7re= 7r*= -n=fO. Thetrajectory is easily described on the basisof the phase diagram.Assume that the economy is initially inequilibrium at the intersection of theEOE6and POP' curves. Then let the rate ofmonetary expansion per effective workeraccelerate from zero to ,u-n= OA > 0 inFigure 5. If expectations change slowly,then the forthcoming inflation is not yetanticipated and z= ,-n-7r*= ,-n-O=,u- n. Graphically, the EE' curve does notshift. Solely for the sake of geometricsimplicity, assume that the coefficient ofz in equation (50) is sufficiently small as to

7T

El

Eo~~~~~~~~~E

FIGURE 5. WHEN THE R{ATE OF MONETARY EXPANSION PER EFFECTIVE WORKER ISRAISED FROM ZERO TO QA, THE ECONOMY FOLLOWS TRAJECTORY OBCA TOTHE STEADYSTATE (xG1, ) = (0, ,~-n). GRAPHICALLYTHE EE' CURVESHIIFTS ALONGP,Pt TO 1E,A (FROMEOEO)


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886 THE AMERICAN ECONOMIC REVIEW DECEMBER 1974be ignored.19 Then the POP' curve willshift up by the full amount of the rise inthe rate of monetary expansion.

Real balances per worker start to rise;and the excess aggregate demand is in-creased. The economy starts to head fromthe origin to the temporary equilibriumpoint T in Figure 5. Why? As a result ofthe rise in real balances, excess demandincreases; and the rate of price change israised. The inflation reduces the growth ofthe real wage, and thereby increases therate of employment. For this reason, xl de-clines and 7r rises as the economy headsfrom the origin to point T.As the inflation proceeds, inflationaryexpectations develop. This means thatz=,-n-7r* decreases. In graphic terms,this means that the EoEo curve starts torise towards E1E', as wage negotiationsare based upon a higher rate of anticipatedinflation. The rising EE' curve impliesthat the economy will eventually head forpoint A, at the intersection of the P1P' andE1EA curves. Trajectory OBCA may de-scribe the motion of the economy to thenew equilibrium point A = (xi, 7r)e (0,g-n).Monetarist conclusions are thereby ob-tained. The monetary acceleration reducedthe unemployment rate temporarily belowthe equilibrium rate. The absolute rate ofmonetary expansion per effective workeronly affects the steady-state rate of pricechange; but there is no relation betweenunemployment rate x1 and the constantrate of monetary expansion per worker atthe steady state. Compare the origin withpoint A. Unemployment can be kept be-low Ue, i.e., xi can be kept negative, only ifthe process is repeated. That is, the rate ofmonetary expansion must be raised stead-ily; and this leads to hyperinflation. This

model can imply monetarist conclusions.If the term [(P4-P1/2)DG+P5DO] werepositive, then "weak monetarist" conclu-sions would follow. A steady rise in govern-ment expenditures (DG >O) financedthrough the sale of bonds would raise therate of price change and reduce the level ofunemployment. The PP' curve wouldshift upwards and intersect the EE' curvein the second quadrant. However, if thelevel of government expenditures thenstabilized (DG =O) but P5

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VOL. 64 NO. 6 STEIN: MONETARISM 887Fed. Reserve Bank St. Louis Rev., Apr.1970, 52, 7-71.K. Brunner, "The Monetarist Revolution inMonetary Theory," Weltwirtsch. Arch.,1970, Part 2, 105, 1-30.and A. Meltzer, "Friedman's Mone-tary Theory," J. Polit. Econ., Sept./Oct.1972, 80, 951-77.0. Eckstein, The Econometrics of Price De-termination Conference, Washington 1972.M. Friedman, "Comments on the Critics,"J. Polit. Econ., Sept./Oct. 1972, 80, 906-50.R. J. Gordon, "Inflation in Recession andRecovery," Brookings Papers, Washington1971, Z, 105-66.E. Infante and J. L. Stein, "Optimal Growthwith Robust Feedback Control," Rev.Econ. Stud., Jan. 1973, 40, 47-60.J. M. Keynes, A Treatise on Money, Vol. I,London 1930.D. Laidler, "Simultaneous Fluctuations inPrices and Output-A Business Cycle Ap-proach,"Economica, Feb. 1973, 40, 60-72.R. E. Lucas, Jr. and L. Rapping, "RealWages, Employmentand Inflation," J. Polit.Econ., Sept./Oct. 1969, 77, 721-54.K. Nagatani, "A Monetary Growth Modelwith Variable Employment," J. Money,Credit,Banking, May 1969, 1, 188-206.D. Patinkin, "Friedman on the QuantityTheory and Keynesian Economics," J.

Polit. Econ., Sept./Oct. 1972, 80, 883--905.E. Phelps, "The 1972 Report of the Presi-dent's Council of Economic Advisers: Eco-nomics and Government," Amer. Econ.Rev., Sept. 1972, 62, 533-39.H. Rose, "Unemployment in a Theory ofGrowth," Int. Econ. Rev., Sept. 1966, 7,260-82.P. Samuelson, "The Role of Money in Na-tional Economic Policy," in ControllingMonetary Aggregates, Monetary Confer-ence, Federal Reserve Bank of Boston,June 1969.J. L. Stein, "Money and Capacity Growth,New York 1971.

and E. F. Infante, "Optimal Stabili-zation Paths," J. Money, Credit, Banking,Feb. 1973, Part II, 5, 525-62.J. Tobin, "'Commentsand Discussion: TheFellner, Okun, and Gordon Reports,"Brookings Papers, Washington 1971, 2,511-14., (1972a) "The WVage-PriceMecha-nism: Overview of the Conference," in0. Eckstein, ed., The Economietricsof PriceDetermination Conference, Washington1972.-- , (1972b) "Inflation and Unemploy-ment," Amer. Econ. Rev. Mar. 1972, 62,1-18., (1972c) "Friedman's TheoreticalFramework," J. Polit. Econ., Sept./Oct.1972, 80, 852-63.

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