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ROBERT M. COEN Northwestern University BERT G. HICKMAN

Keynesian and Classical Unemploymentin Four Countries

THE WORLD entered a period of stagflationduring the 1970s. Markedly slower growth combined with rates of and inflationthat were unprecedentedlyhigh for the postwar era, and the slowdown persists to this day. In this paper we draw on a larger study of the deceleration of potential growth to emphasize the contributory role of demandshortfalls in prolongingand deepeningthe adjustmentto lower growth rates of productivityand real . A key issue is the relative importanceof high and deficient aggregatedemand as proximatecauses of the rise of unemployment. We use the theoreticalapproach developed by Hickmanto estimate the classical and Keynesian componentsof excess unemploymentin the , , Austria, and the .1The ap- proach is closely related to the " gap" analysis of

This paperis partof a researchproject on unemployment,real wages, and economic growthin selectedOECD countries. The supportof the AustrianNational is gratefully acknowledged.We are indebtedto the BrookingsPanel and to Erich Streissler, Stefan Schleicher,Stephen King, GeorgeEvans, Jean Waelbroeck,and seminarparticipants at the Universityof Vienna,Project LINK, and StanfordUniversity for theircomments and suggestions.Thanks are also due to ChristianStadlinger for his valuableassistance. 1. BertG. Hickman,"Real Wages, Aggregate , and Unemployment"(Center for EconomicPolicy Research, Stanford University, July 1986).Forthcoming in European Economic Review.

123 124 Brookings Papers on Economic Activity, 1:1987 andJeffrey Sachs, butit differsin buildingon the assumptionof imperfect competitionand cost minimizationrather than perfect competitionand profitmaximization as the basis for .2Similarly, it differs fromthe generaldisequilibrium or non--clearingmodels of Robert Barroand Herschel Grossmanand EdmondMalinvaud in that it allows for coexistence of classical and Keynesian unemploymentinstead of explainingthem as separateregimes in marketswith -takingfirms and rationedbuyers and sellers.3 Our empirical measures of the wage and demand components of are computed from a conditional demand function for aggregateman-hours, with the real wage and outputtreated as predeter- mined to the employment decisions of firms. Since the real wage and aggregatedemand are in realityendogenous variables, the decomposition deals only with their relative importance as proximate sources of unemployment.A deeper approachwould employ a complete macro- endogenizing aggregate output and real wages and capable of explainingthe evolution of both as a function of exogenous shocks to aggregate and demand, as recommendedby .4 That would be feasible in our U.S. model, which is just such a complete system, but not in the truncatedsupply-side models we have estimatedfor the Europeancountries in the study.

Concepts of Keynesian and Classical Unemployment

The standardfixed-price or non-market-clearingmodel distinguishes Keynesianand classical unemploymentstates as separateregimes under fixed wage and price levels by incorporatingquantity constraints into the optimizationproblems of firmsand .5

2. Michael Bruno and Jeffrey D. Sachs, Economics of Worldwide (Harvard UniversityPress, 1985). 3. RobertJ. Barroand Herschel I. Grossman,"A GeneralDisequilibrium Model of Incomeand Unemployment,", vol. 61 (March1971), pp. 82- 93; , The Theory of Unemployment Reconsidered (Oxford: Basil Blackwood, 1977). 4. Robert M. Solow, "Unemployment:Getting the Questions Right," Economica, vol. 53 (Supplement,1986), pp. S23-S34. 5. Basic references include , , and : An Integration of Monetaryand Theory,2d ed. (Harperand Row, 1965);Robert Clower, "The Robert M. Coen and Bert G. Hickman 125 The representativefirm is a price taker in its marketsfor inputs and output. It maximizes profits subject to a well-behaved function, Y = F(K,L), and a product demand constraint, Y c Y. For fixed K in the short run, the optimalsolution for L is the min-equation

(1) Ld = min[F- 1 (Y,K), FL 1 (WIP,K)], where WIPis the real productwage. The unconstrainedor notional short-runfunctions for labor demand and productsupply are

(2) Ld = FL1 (WIP,K), given by the first-ordermarginal condition, and

(3) ys = F(Ld,K). The classical labor supplyfunction is (4) Ls = Ls(W/P), where the real wage equates the marginaldisutility of effort and the marginalutility of consumption. With flexible wages and prices, a Walrasiansolution of equations 2 and 4 would yield at the equilibriumreal wage. With fixed wages and prices, however, if notional supply exceeds effective demandat the given price, the sales of firmsare rationedin the product market. Labor demand is then output-constrainedand is smaller than laborsupply at the existing real wage, resultingin Keynesianunemploy- ment: (5) Ld = F-1 (Y,K) < Ls (WIP). Thus Keynesian unemploymentis the effect of disequilibrium in the productmarket. Classical unemploymentmay occur if the fixed price is below the Walrasianequilibrium level. then exceeds notional

KeynesianCounterrevolution: A TheoreticalAppraisal," in F. H. Hahn and F. P. R. Brechling, eds., The Theory of Interest Rates (London: Macmillan, 1965), pp. 103-25; Barroand Grossman, "A General DisequilibriumModel"; Malinvaud,The Theoryof UnemploymentReconsidered; Jean-PascalBenassy, "Neo-Keynesian Disequilibrium Theory in a Monetary Economy," Review of Economic Studies, vol. 42 (October 1975), pp. 503-23; Jean-Pascal Benassy, The Economics of Market Disequilibrium (Academic Press, 1982). 126 Brookings Papers on Economic Activity, 1:1987 supply. Firms have no incentive to increase supply at the existing real wage, so the short side of the market prevails and households are rationed.Firms are unconstrainedand operatingon their notionallabor demandand output supply schedules, but since the real wage exceeds the Walrasianlevel, labor demandfalls short of full-employmentlabor supply. In both unemploymentstates householdsare constrainedin the labor market, and hence effective demandfalls short of the notional demand that would result from unconstrainedutility maximization.Indeed, as Robert Clower showed, it is because of the spillover from the labor market constraint that is an argument in the consumption function.6 However, the approach of this paper modifies the standardfixed- price model, in which prices are fixed over the periodbeing analyzed, in two principal respects. First, we assume imperfect with firms setting prices in the face of uncertain demand. We assume that prices are not continually adjusted. Second, firms choose and labor inputs so as to minimize the cost of producingthe quantitythey expect to sell at the price they have set. The assumptionof imperfectcompetition is adoptedfor both theoret- ical and empiricalreasons. Perfect competitionamong atomistic price- takingfirms is incompatiblewith the fixed-priceassumption except for very shortadjustment periods afterunexpected shocks. As an empirical matter, moreover, auction markets are largely limited to agricultural productsand primarymetals. There is also solid econometricevidence of the ubiquitousexistence of cost-basedprice setting,with only a limited scope for markupvariations in response to shifts in productdemand.7 One important consequence of cost-based price setting is that it reduces the sensitivity of real wages to changes in effective demand. Increases or decreases in nominalwages induced by shifts in aggregate demandinduce price movements in the samedirection, greatly mitigating the response of real wages to demand pressures in labor markets. In contrast, supply shocks that directlyraise productioncosts, such as the 6. Clower, "The KeynesianCounterrevolution." 7. Otto Eckstein, ed., TheEconometricsofPriceDetermination, conference sponsored by Board of Governors of the System and Social Research Council(Board of Governors, 1972);Phillip Cagan, "The Hydra-HeadedMonster: The Problemof Inflationin the UnitedStates," DomesticAffairs Study 26 (,D.C.: AmericanEnterprise Institute, 1974); William D. Nordhaus,"The Falling Share of Profits," BPEA, 1:1974, pp. 169-208. Robert M. Coen and Bert G. Hickman 127 energy shocks of the 1970s, have greater potential to alter real wage rates unless they are offset by promptand substantialwage indexation. As a corollaryto real wage inflexibilityunder markup , macro- economic models, includingour own, that incorporatethe hypothesis generallydepend for theirequilibrating on absolutevariations in the wage-pricelevel, operatingthrough the Phillipscurve and markup mechanisms. In the standard textbook IS-LM model, for example, restoration of long-term equilibriumafter a shock depends on price- inducedchanges in the real money supplyand interestrates.8 In some of the largereconometric models, real argumentsin the aggregate demandfunctions are also involved.9 Market imperfectionsprovide a theoretical rationale for the fixed- price assumption.One theoreticalrationale is the perceived asymmetry of competitors'responses to a firm'spotential price increaseor decrease in oligopolistic industries as the source of price rigidity, as in Paul Sweezy's theory of the kinked .10Similarly, in 's conjecturalequilibrium model of atomisticfirms, a kink in the perceived demandschedule exists because of the asymmetricreactions of consumersto price changes: "Lower prices asked by a suppliermay not be fullyadvertised to customerscurrently buying from other suppliers who are maintainingtheir currentprice, while a higherprice chargedby the same supplier necessarily induces present customers to leave in search of lower price suppliers."II Imperfect informationand search

8. See, for example, RudigerDornbusch and , ,3d ed. (McGraw-Hill,1984); Robert J. Gordon, Macroeconomics, 3d ed. (Little, Brown, 1984); Robert Hall and John Taylor, Macroeconomics: Theory, Performance, and (Norton, 1985). 9. The equilibratingmechanisms in empiricalmultinational models are discussed in Bert G. Hickman, The U.S. Economy and the International Transmission Mechanism: A Structural Comparison of Twelve Multicountry Models, CEPR Publication 78 (Center for EconomicPolicy Research,Stanford University, 1986);those in U.S. econometricmodels are discussed in Hickman, "Macroeconomic Effects of Energy Shocks and Policy Responses: A StructuralComparison of Fourteen Models" (EnergyModeling Forum, StanfordUniversity, 1984). 10. Paul M. Sweezy, "Demandunder Conditions of ,"Journal of ,vol. 47 (August1939), pp. 568-73. 11. Takashi Negishi, Microeconomnic Foundations of Keynesian Macroeconomics (Amsterdam:North-Holland, 1979), p. 87. FrankH. Hahn'smodel of conjecturalequilib- riumis similarto Negishi's but does not assume a kink in the perceiveddemand curve. See Hahn, "Exercises in Conjectural Equilibria," Scandinavian Journal of Economics, vol. 79 (1977),pp. 210-26; Hahn, "On Non-WalrasianEquilibria," Review of Economic Studies,vol. 45 (February1978), pp. 1-17. 128 Brookings Papers on Economic Activity, 1:1987 processes are also central to ArthurOkun's customer shoppingmodel, with added on the desire of sellers to maintainstrong long-term customerattachment to theirproducts by forgoingprice adjustmentsto temporarydemand fluctuations.12In all these formulations, shifts in demandinitially lead to a changein the quantitysold at the currentprice and may leave the price permanentlyunaffected; thus they provide a justificationfor the fixed-priceor rigid-pricemodel that is used here. Under imperfectcompetition, the firmexpects to sell output Ywhen it sets price at P. Expected revenue is predetermined,and the firm minimizesproduction costs to determinefactor . For fixed K, L will againbe given by the invertedproduction function as in equation 5. If substitutionof capitaland laboris taken into account, however, the labor demandfunction becomes conditionalon the wage-rentalratio as well as on output:

(6) Ld = Ld (W/Q,Y). The replacementof the invertedproduction function in equation5 by the conditionallabor demand function, equation6, is the key to the new methodof allocatingunemployment in this paper. Since the rentalprice of capital, Q, includes the price of capital (P1) along with the discount and rates, labor demand depends on the real investmentwage (WIPI),as well as on output, in contrastto the discrete classical and Keynesian dichotomy in equation 1. Labor demand can therefore fall short of full-employmentlabor supply because effective demandis too low or becausethe realwage is too high,or both. Keynesian and classical unemploymentmay coexist ratherthan occurringin sepa- regimes as in the standardfixed-price disequilibrium model. Clas- sical unemploymentis ruled out as a discrete state with firms on their notional supply schedules and households rationed off their demand schedules, but it may still occur in the absence of Keynesianunemploy- ment providedthat a positive wage gap-with the real wage above the full-employmentlevel-exists withoutan accompanyingdemand short- fall. We follow established terminology in referring to unemployment attributableto a positive wage gap as classical and unemploymentdue to deficienteffective demandas Keynesian. It is truethat our imperfectly 12. Arthur M. Okun, Prices and Quantities: A Macroeconomic Analysis (Brookings, 1981),p. 87. Robert M. Coen and Bert G. Hickman 129 competitive setup allows for the coexistence of both components, but that is not fundamentallydifferent from the Keynesian state of the competitive model, which requires only that firms be demand-con- strained,so thatemployment is determinedfrom the invertedproduction functionunder the min-conditionin equation1. If, in additionto a binding demandconstraint, the real wage also exceeds the Walrasianlevel in the competitive model, restorationof full employmentwill requirethat the real wage gap as well as the demand gap be eliminated. This is the distinctionmade by Barro and Grossmanbetween Keynesian involun- tary unemploymentdue to inadequate product demand with the real wage at or below the Walrasianlevel, andany latentclassical involuntary unemploymentdue to a concurrentwage gap.13Similarly, Jean Pascal Benassy notes thatin the foregoingcircumstance, it would be necessary to increase aggregatedemand and decrease the real wage to suppress unemploymenttotally, so that "both classical and Keynesian measures would be necessary." 14 Thereare nonethelessimportant differences between the competitive model and our approach.In the classical unemploymentregime of the competitive model, a positive real wage gap forecloses any increase of employmentfrom expansionary demand . Excess demandexists for goods, and any additional demand stimulus could not improve employment, since profits are already maximizedat the currentwage- price configurationand capitalstock. Similarly,if an inflexiblewage gap accompaniesthe Keynesian demand-constrainedregime, the classical componentof excess unemploymentcannot be eliminatedby a demand stimulus. In the imperfectlycompetitive model, by contrast, the labor demand functionis shifteddirectly by changes in output, and hence the classical componentof unemploymentcan be offset by high effective demand,as happened often in Austria and occasionally in the United States and Germanyaccording to our empiricalresults. A positive wage gap is not necessarilyan impenetrablebarrier to eliminatingexcess unemployment by demandmanagement, although there may be limitationsand draw- backs to such a policy, as discussed later. The differencein the assumptionabout whetherthe real wage affects output makes a big difference to the of employment with 13. Barroand Grossman,"A GeneralDisequilibrium Model," pp. 86-87. 14. Benassy, The Economics of Market Disequilibrium, p. 130. 130 Brookings Papers on Economic Activity, 1:1987 respect to the real wage. As will be shown later, employmentis much more responsive to a wage change underthe competitivecase. To elucidate key features of our approach,it is best to abstractfrom complicating aspects of the empirical models. Let us assume, for simplicity,that the full-employmentlabor supply is exogenously given. The magnitudeof classical unemploymentthen depends on the size of the real wage gap and on the elasticity of labor demandwith respect to the real wage. To establish the size of the wage gap, we must first determinethe full-employmentequilibrium value of the real wage and the correspondinglevel of output-that is, potentialoutput. Our concept of full-employmentequilibrium is based not on labor marketclearance at a given capital , as in the short-runcompetitive model above, but on capital as well as labor marketequilibrium. That is, it assumes that profits would be maximized if firms were operating at the full- employmentequilibrium. The full-employmentreal wage must be con- sistent not only with full employmentof labor but also with attainment of a requiredmarginal rate of returnon capital. The natureof the full-employmentequilibrium is most transparentif we neglect technicalprogress and expectationaland adjustmentlags, all of whichplay importantroles in ourempirical models. As in the empirical models, we assume that the aggregate is Cobb- Douglas with constantreturns to scale: (7) Y= KaLl-o. Firmschoose inputsto minimizecosts, so that the optimalinputs satisfy the expansionpath equation:

(8) W/Q = [(1 -ot)/ot](KL), where Q is the implicitrental price of capital. If there are no , and if there is a homogeneousoutput that can eitherbe consumedor be used as capital, then Q = P(R + d), where P is the price of output, R is the rate of returnon capital, and d is the depreciationrate. Then equation8 can be writtenin terms of the real wage as

(9) WIP = [(1 - o0)/oi(K/L)(R + d). In an imperfectlycompetitive equilibrium,the value of output exceeds total factor costs, and national income can therefore be expressed as PY = A [WL + QK], where X > 1 and depends on the price elasticity Robert M. Coen and Bert G. Hickman 131 of demand. Solving the nationalincome equationfor the rate of return, we obtain

(10) R = (PY - XWL APdK)/APK- = (Y/XK) - (WL/PK) - d. Substitutingfrom equation9 for (WL/PK)gives

(11) R = ot(Y/XK)- d. Thus the returnR equals the marginalrevenue productof capitalnet of depreciation. Setting R = r, the required rate of return, and L = LJs,the given full- employment labor supply, equations 7, 9, and 11 determine the full- employmentreal wage, potentialoutput, and potentialcapital, the latter being the capital stock that yields the returnr when employmentis Ls and the real wage satisfies equation 9. Denoting the solution values by asterisks, we have (12) Y* = [oJA(r + d)]a/(la-)Ls

(13) K* = [otA(r + d)]1/(1 - )LS

(14) (W/P)* = (1 - ox)[ox/(r+ dJ]a/(1a) (/-

The smaller the required return on capital and the larger the full- employment labor supply, the larger are and capital stock. The equilibriumreal wage also depends inversely on the required return,but it is independentof the exogenous labor supply. It is easy to show that the right-handside of equation 14equals the marginalrevenue product of labor, (1 - x)(Y/XL). The full-employmentequilibrium is depictedgraphically in figure 1.15 The isoquant labeled YO*refers to potential output and the equilibrium inputsare KO*and Ls = L*, satisfyingthe cost-minimizingcondition that the marginalrate of technical substitutionbetween L and K equals the wage-rentalratio, (W/P)*[I/(r + d)], or geometricallythat the slope of the isoquantequals the slope of the isocost line tangentto it at point A. The ray throughA is the expansion-pathlocus for which the same factor proportionsare optimal for the same wage-rentalratio at any scale of output.

15. We are gratefulto JamesTobin for discussionsthat clarifiedthe analysis and led us to use this figure. 132 Brookings Papers on Economic Activity, 1:1987

Figure 1. Theoretical Model of Components of Unemployment

Capital

yI

K3 H

E K2 C F D I A

B K,

L2 LI L3 L*Labor

Suppose now that the economy is operatingat point E on the lower isoquant labeled Y1 but at the higher wage-rental ratio, given by (WIQ)1= (WIP),[1I(r + d)] and indicatedby the higherray throughE. The new cost-minimizinginputs are relatedto outputby the conditional factor demandfunctions:

(15) L2 = [ci/(1 - 0X)]at (WIQ)v a Y1,

(16) K2 = [a/(1 - c )]1- (I/Q)(i-o) y (We are momentarilyneglecting lagged adjustments of factor inputs.) In this situationthe observed wage gap is (WIP), - (WIP)*and unemploy- ment equalsLo - L2. How responsivewould employmentbe to a reductionof the realwage to (WIP)*?The answer is crucial, since it determines the estimated amountof classicalunemployment for the given wage gap. One approach Robert M. Coen and Bert G. Hickman 133 would be to measurethe employmentchange conditionalon the level of capitalstock at E, as in the short-runcompetitive model. Withinstanta- neous laboradjustment and an unconstrainednotional supply , the short-runwage elasticityof labordemand is - (1/x) andthat of output supply is - (1 - ox)/oxunder the Cobb-Douglas . Thus, given a reasonable value of 0.25 for ox,the implied labor elasticity would be -4. This large elasticity reflects the substantial short-runsupply re- sponse of competitivefirms (with ot = 0.25, a 1 percent reductionin the real wage increases the supply of output by 3 percent) and implies employmentgaps several times the associated wage gaps. The crucial point is that these largeresponses would occur only if competitivefirms were actually on their notional supply schedules in a regime of excess demand and that the wage gap would then be the sole cause of unem- ployment. In contrast, with the demand constraintprevailing under imperfect competitionand labor demand conditional on output,as in ourbehavioral interpretationof point E, a decline in the real wage from (WIP), to (WIP)*would lead firmsto raise employmentto LI, associatedwith point B on the Y1isoquant. Thus, our estimate of classical unemploymentis LI - L2; this is the amount that could be eliminatedby removing the wage gap, given the level of . To eliminate the remainingunemployment, Lo - L1, a higher level of aggregatedemand is needed; hence, we refer to this component of unemployment as Keynesian. Fromour specificationof the labordemand function, equation 15, the wage elasticity of labor demand is -ac rather than -(l/ox), or -0.25 ratherthan - 4. Classicalunemployment from an excessive real wage is still possible and may even be dominant, but the coexistence of wage and demand components of unemploymentis to be expected, and the division will depend on the particularconfiguration of real wages and effective demand.Despite the "small" elasticity, the realwage gap may be large enough to dominateexcess unemploymentoccasionally or for severalyears at a time, as will be shown in the empiricalresults. Several importantobservations need to be made about our decom- position of unemployment.First, the measure of each component is a conditionalestimate. The classical component assesses the effect of a lower real wage, conditionalon the observed level of demand;it does not allow for possible effects of a reduced real wage on Saggregate 134 Brookings Papers on Economic Activity, 1:1987 demand.Similarly, the Keynesian componentassesses the impactof an increase in aggregatedemand, conditionalon the real wage being at its full-employmentequilibrium level; it does not allow for possible effects of an increase in aggregatedemand on the real wage. By contrast, the classical componentof unemployment,as usually defined, includes the effects of high real wages in reducingthe quantityof output that firms are willingto supply and the relatedemployment. Second, the analysisdoes not identifythe disturbancesthat depressed aggregatedemand, raised the realwage, andthereby moved the economy fromA to E. The definitionsof the classical and Keynesian components of unemploymentrefer to the state or existence of the real wage and demandgaps and not to the exogenous or endogenous forces creating the gaps. As one illustration, assume that an exogenous increase of money wages occurs at potential output without any adjustmentof the (contrary to markup pricing behavior) or real aggregate demand.Classical unemployment would then occur as employmentfell along the conditional labor demand schedule for potential output, or equivalently, employment would fall from Lo to L3 as the economy moved to point H on the potentialisoquant. Now assume instead that a nominalwage shock induces a less-than-proportionalincrease of prices in (at least) the short run (perhapsbecause invariantprice markupsare based on normalinstead of currentunit labor costs), so that the same rise in the real wage rate is accompaniedby a higherprice level. Withan unchangedmoney supply, the induced decline of real balances would reduceeffective demandand shift the labordemand function downward, addinga Keynesian component of unemploymentto the classical one, or equivalently, moving the economy to, say, point E on the lower isoquantwhere employmentwould be L2instead of L3.Thus Keynesian unemploymentcan arisefrom an unaccommodatedsupply shock, owing to an inducedchange in effective demand.Conversely, an expansionary monetaryor to reduce Keynesianunemployment may itself inducea decreasein the realwage andclassical unemployment, provided nominalwages are incompletelyindexed-or the reverse could occur if indexation is complete and the price markup varies strongly with demand.16

16. On this point, see JeffreySachs, "Real Wages and Unemploymentin the OECD Countries,"BPEA, 1:1983,pp. 255-89, for an argumentand supportingevidence that a demandexpansion would probablyraise real wage growthin Europeunder the conditions prevailingat the time. Robert M. Coen and Bert G. Hickman 135 Third, although it is true that at points A, B, E, and H firms are employing cost-minimizinginputs for the given levels of demand and factor prices, only A is a full macroeconomicequilibrium. Clearly the labormarket is in a state of at the other points. But points E and H have an additionaldefect in that the realized rate of returnon capital is smallerthan the requiredrate. To see this latter point, recall that the realizedrate of returnis proportionalto the output-capitalratio, since the marginal product of capital is ox(YIK).With our assumed technology,the output-capitalratio is monotonicallyrelated to the labor- capitalratio. Since the labor-capitalratio is smalleralong the ray through E and H than the ratio along the ray throughB and A, the realized rate of returnmust also be smaller.17 In our imperfectly competitive frameworkin which firms are price setters, failureto realize the desiredrate of returnshould lead producers to raise prices. If wages are imperfectlyindexed to prices, the wage gap may be narrowedand the realized rate of returnincreased. However, the rise in the absolute price level may further depress the level of aggregatedemand through Keynes and Pigou effects. While a complete macroeconomicmodel is obviously requiredto tracethese repercussions of a wage gap, the less apparentpoint to note is that classical unemploy- ment presents a more complicatedproblem of macroeconomicadjust- ment thandoes Keynesianunemployment. If the economy were at point B experiencing only Keynesian unemployment, the required rate of returnwould be realized, since the labor-capitalratio is the same at B and A. A demand stimulus that left the real wage unchanged could restore equilibriumin both the laborand capitalmarkets. By contrast, if the economy were at E, a demand stimulus that left the real wage unchangedcould reduce the excess supply of labor, but it would not correctthe deficiencyin the rate of return. Fourth, the absence of adjustmentlags in the foregoing exposition permits no distinction between short-runand long-run factor adjust- ments. However, adjustmentlags are central features of our empirical models and substantiallyaffect our estimates of classical and Keynesian

17. If there are separateprices for finaloutput and capitalgoods, as in our empirical models, then the realized rate of return would be R = ot(PIPI)(YIXK)- d, where PI is the capitalgoods price , and P is the price of finaloutput. In this case, R could remain unchangedat a lower output-capitalratio if the relative price of capitalgoods declined sufficiently. creditsor other subsidiescould also be used to reducethe real rentalrate while preservingthe real rate of returnat a highercapital-labor ratio. 136 Brookings Papers on Economic Activity, 1:1987 unemployment.To illustrate,consider once againfigure 1. Suppose that the economy is operatingunder conditions of full-employmentequilib- rium at point A, producing the potential output YOwith the optimal inputs Lo and KO.Assume that a reduces output to Y1 withoutaffecting the real wage, so that the new desiredinputs are given by K1and L1at point B. If the short runis definedas a periodin which K cannot change and L fully adjusts, realized labor input would drop to point C, overshootingthe long-rundesired level, and Keynesian unem- ployment would equal A - C. In other words, full equilibriumwould requirea decrease in K to move the economy to B, so that "long-run" Keynesianunemployment is overstatedat point C. Since an equilibrium at C would requirea higherwage-rental ratio than at B, the horizontal distance between B and C is a kind of latent classical unemployment correspondingto a latent wage gap. If an actual wage gap accompanied the demandgap, moreover, so that full equilibriumwere at E with labor inputL2, the true classical unemploymentcomponent would be L1 - L2 rather than the horizontal distance between C and L2, and classical unemploymentwould be understatedby the same amountas Keynesian unemploymentwas overstated. If one assumes, as we do, however, that adjustmentcosts induce firmsto adjusttheir labor inputs only partiallyin a given year, Keynesian unemployment will not overshoot. Moreover, any existing classical componentwill always be observable.In the purelyKeynesian case, for example, only part of the gap between Lo and L1 is closed and unem- ployment is equal to, say, A - D. Now assume that the real wage also increases when output drops. This could occur independentlybecause of a wage or price shock, or it could be induced by the originalfall in aggregatedemand. In any event, the new desired inputs would differ andmight be given by a pointlike E. If we againassume partial adjustment of the gap between the initial and the desired labor inputs, actual employmentwill be at point F, smallerthan D. Total unemploymentis A - F, of which the Keynesian component is A - D and the classical share isD - F. Note that owing to adjustmentcosts, the observed, measuredquan- tities of K and L are not constrainedto be on the productionfunction in this system. However, the effective inputs of capital and labor services must be sufficientto produce the observed output. A given quantityof observed labor input, as measured for example by man-hours, may Robert M. Coen and Bert G. Hickman 137 representa greateror lesser amountof labor services or effective input when a man-houris used moreor less intensively,for exampleby altering the pace at which employees or the numberor durationof leisure breaksduring a work shift. There is an additionaldegree of freedomfor capitalinput, since the measuredcapital stock may be operatednot only faster or slower per hour but also more or fewer hours per week. Thus, variationsin the intensity of factor utilization (effective flow of factor services per measuredunit of input) occur in the process of adjusting measuredinputs towardthe desired quantities.On the assumptionthat a firmincreases its employmentof a factorbecause it is using the current amountof the factor at greaterthan normalintensity, we posit that the intensitiesof utilizationof K and L are proportionalto the discrepancies between the observed and desired magnitudes.18 Hence, if measured inputsare at point D while desiredinputs are at point B, both capitaland labor are underutilizedbecause firms would like to reach a position in which they have less of both; if measuredinputs are at point F, while desired inputs are at point E, labor is underutilized but capital is overutilized. Thus far we have focused on labor input, but the capital stock will also adjust partiallytoward the new desired value given by K, or K2. Some investment or disinvestment would occur on impact, but any incrementalstock is assumed not to become operative until the end of the year, and similarlyany discards are assumed to occur at the end of the year, so that actual K is still fixed at Ko insofar as the production function is concerned. Meanwhile, the acceleratoreffect of the output reductionwill tend to decrease currentinvestment whereas the substi- tution effect of the higherwage-rental ratio will tend to increase it. 19As drawnat point E, the substitutioneffect is largerand net investment is positive. If the increase in the wage-rental ratio were smaller than assumedin figure 1, however, so that K2and L2were at a point such as G along a lower expansion path, the output effect would be dominant andinvestment would decrease on balance. In actualpractice, an output shortfallis apt to occur because rising currentoutput lags the growing potentiallevel, instead of falling absolutely as was assumedfor exposi-

18. Bert G. Hickman and Robert M. Coen, An Annual Growth Model of the U.S. Economy(Amsterdam: North-Holland, 1976), pp. 12-17. 19. The positionof the lowerisoquant must be consistentwith the inducedinvestment in the solutionof the completemodel. 138 Brookings Papers on Economic Activity, 1:1987 tional purposesin figure 1, so that both observed K and observed L will usually lag the equilibriumquantities and net investmentwill usually be positive. Let us now trace throughthe effects of a real wage shock of the same size as before, so as to avoid the need for clutteringthe diagramwith another expansion path ray, but this time disturbingthe originalfull- employment equilibrium.If aggregatedemand is unchanged, the new equilibriumwill be at H and the partial adjustmentof L would carry employmentto a point such as I, generatingclassical unemploymentof A - I. If the real wage increase were accompaniedby an independent or induced change in aggregatedemand and output, however, the new equilibriumwould be along the expansionpath through H but on a lower isoquant. For graphicalconvenience only, it is assumed that the lower isoquantis againat Y1and the desired inputs are againgiven by point E. Totalunemployment would then againbe A - F, with a Keynesian share of A - D and a classical component of D - F (smaller than A - I because the same proportionalwage gap as on the lower isoquant between E and B is applied to a larger output between H and A). The example is restrictivein that the wage and demandgaps would be equal only by accident when the wage gap was induced by a demand shock and the demand gap by a wage shock, but it serves conveniently to illustratethe propositionthat the concepts of classical and Keynesian unemploymentrefer to economic states rather than to the shocks or responses that producedthem.

An Empirical Disequilibrium Growth Model

Empiricalimplementation of our approach to factoring Keynesian and classical unemploymentrequires the specification of a dynamic structuralmodel of the labor marketand of the full-employmentpath of outputand the real wage. For the United States, we rely on the relevant sectors of the Hickman-Coen Annual Growth Model, including its structureof interrelatedfactor demands, its disaggregatedmodel of labor supply, and its model of the naturalgrowth path of potentialoutput.20

20. RobertM. Coen and Bert G. Hickman,"Constrained Joint Estimationof Factor Demand and Production Functions," Review of Economics and Statistics, vol. 52 (August 1970),pp. 287-300;Hickman and Coen, An AnnualGrowth Model; Coen and Hickman, "A DisaggregatedModel of Labor Supply and Unemployment, 1951-2000,"Working Robert M. Coen and Bert G. Hickman 139 Although the U.S. model is a complete macroeconomic system combiningKeynesian and neoclassical elements and allowingfor depar- turesfrom the full-employmentgrowth path owing to deviationsbetween effective demandand supply, the new Europeanmodels are confinedto the supply-side equations and treat aggregate demand and the wage- price level as exogenous variablesfor the purposes of the labor market .Correspondingly, the empiricalresults for the United States arederived from stand-alone simulations of the laborsector of our annual growthmodel, with expected outputand the expected real wage treated as predeterminedvariables in the labordemand function. The derivation is justifiablebecause the behavioralassumptions of the model conform to the imperfectlycompetitive paradigm of the precedingsection. Firms set their prices as a markupover normalunit laborcost, with allowance in the markupfor the costs of importedinputs and the currentlevel of . For the given prices, output is determined by effective demand,which is disaggregatedinto three categoriesof invest- ment, six of consumption,federal and state andlocal purchases,exports, and imports. Nominal wages are determinedby an expectations-aug- mented . Since this paper is not concerned with output determination,the -unemploymenttrade-off, or the absolute price level, none of these sectors is operational in the subsequent analysis. The following sections describe the general forms of the empirical equations of the U.S. model and note differences between the U.S. equationsand those of the Europeannations. Estimatesof key parame- ters and elasticities are also reported.The data are brieflydescribed in footnotes to the tables and text. A full listing of the estimatedequations and their statisticalproperties is availablefrom the authors.

The Labor Market

LABOR SUPPLY The U.S. model contains labor force participationequations for sixteen age-sex groups, of the form

Paper80-15 (Institute of AppliedSystems Analysis, Laxenburg,Austria, January 1980); Coenand Hickman,"The NaturalGrowth Path of PotentialOutput," Working Paper 80- 132(Institute of AppliedSystems Analysis, Laxenburg,Austria, August 1980). 140 Brookings Papers on Economic Activity, 1:1987

(17) Lit = NNIit [alIE + a2,i (E/NNI)t + a3,i (LAINNI)t + a4,i(WATIPC)t + a5,AHt + a6,it + a7, NMRATjI, whereLi is the laborforce and NNIi the populationin the ith group, E is aggregateemployment, NNI is the noninstitutionalpopulation sixteen years of age or older, LA is the numberof persons in the armedforces, WATis the after-taxwage rate, PC is the implicitdeflator for goods, AH is aggregateaverage hours of work, t is a time index, and NMRATis the ratio of males aged sixteen to thirty-fourto those aged thirty-five to sixty-four. The ratio E/NNI captures the discouraged workereffect, whereas NMRATis includedin the female participation equationsonly, in conformitywith the hypothesis that increases in this ratio affect the participationrates of younger women positively and of older women negatively.21 The single equationfor average hours in the United States takes the form (18) AHt = exp[b1 + b2l0g(WATIPC)t+ b3logUt + b4logLWt], where AH is average hours per year, U is the unemploymentrate, and LWis the proportionof women aged twenty and over. Workers'desired hoursare assumedto dependon the wage rate, but cyclical variationsin labordemand, proxied here by the unemploymentrate, may affect actual hours. Average hours may also vary inversely with the proportionof women in the labor force, since women are more likely than men to engage in part-timework. The labor supply model is completed by summingover the relevant age-sex participationequations to obtainL and LW. The samegeneral specification of laborsupply is used for the European countries,except thatthe demographicdisaggregation differs, the armed forces variableis droppedfrom equation 17, and the cyclical unemploy- ment variable was found to be insignificantin the hours equations for Austriaand Germany.

LABOR DEMAND The demandsfor laborand capitalare interrelatedin the model, since they arejointlyderived on the assumptionthat firms minimize production

21. Richard A. Easterlin, What Will 1984 Be Like? Socioeconomic Implications of Recent Twistsin Age Structure(Columbia University Press for the National Bureauof EconomicResearch, 1978). Robert M. Coen and Bert G. Hickman 141 costs subjectto along-runorplanning Cobb-Douglas productionfunction with constantreturns to scale: (19) XNR * = AeP (K*)a (MHt*) a, A,ot4 > O, whereXNR* is expected output,K* is the desiredstock of ,22 MH* is desired man-hours,and 13is the rate of Hicks-neutraltechnical progress. Minimizingproduction cost subjectto equation 19 gives the long-run factor demandfunctions:

(20) MHt = [o(1 - ox)]-a A -[(W*IQ*)t] -Y XNR* e - Pt and

(21) Kt = [o(l - o)] -I A -[(W*IQ*)t]( -o) XNRt e -Pt, where Q* is the expected implicit rental price of capital and W* is the expected nominal before-tax wage rate. The implicit rental price is definedby Q PI (r + d) T, where PI is the investmentprice deflator,r is the after-taxrate of return,d is the depreciationrate, and T symbolizes the tax treatmentof investmentexpenditure.23 Adjustmentcosts preventfirms from accommodatingimmediately to variationsin the desiredinputs. These adjustmentcosts includeexternal purchasecosts andinternal installation costs for capitalgoods andhiring, ,and costs for labor. They are representedimplicitly by exponentialpartial adjustment processes:

(22) MHt/MHt-I = MHt*I(MHt_1)f, 0 < f 1,

22. Measuredby nonresidentialfixed capital for the United States and total fixed capitalfor the Europeancountries. See footnote a, table 15, for detailedsources. 23. For all countries, the capital goods price index is the implicitdeflator for gross investment; the economic depreciationrate is the same as that used in constructing estimates of net capital;and the discount rate is 6 percent per annum.Tax parameters requiredin the measurementof the rentalcost are based on tax legislationfor the United States. For Germany, these parametersare adaptedfrom PatrickArtus, Pierre-Alain Muet,Peter Palinkas, and Peter Pauly, "TaxIncentives, , andInvestment in Franceand Germany,"in G. de Menil and U. Westphal,eds., StabilizationPolicy in and Germany(Amsterdam: Elsevier Science Publishers,1984); Mervyn A. King and Don Fullerton, eds., The Taxation of Income from Capital: A Comparative Study of the United States, the United Kingdom, Sweden, and (University of ChicagoPress, 1984).For Austria,they are adaptedfrom a studyby KarlAiginger, "Die industrieinvestionen in Oesterreich, 1955-1980," Industrieinvestionen in Oesterreich, Band 7/8 (Vienna: OesterreichInvestitionskredit Aktiengesellschaft), pp. 7-152, and subsequentupdates to that study suppliedby the author.Under British tax laws, muchof investmentcould be expensedratherthan depreciated. For simplicity,we assumecomplete expensing,in which case tax parametersdo not appearin the rentalcost. 142 Brookings Papers on Economic Activity, 1:1987

(23) KtIKt_1 = K*I(Kt-,)g, O

(25) K, = {[a/o(1- a)] -o A - l [(W*IQ*)t] lt XNR * e -Pt'} Ktll. Because man-hoursand capital adjust with lags to changes in the desired quantities,the observed inputs may be over- or underutilizedin currentproduction, and hence the short-runproduction function in the model allows for variationsin the intensity of use of measured capital and labor inputs. The rates of factor utilizationare determinedendoge- nously by the factor adjustmentprocesses.24 The procyclical behavior of measuredlabor productivity is also explainedby the laggedadjustment of man-hoursto changes in output. Joint estimation of the short-rundemand functions yields estimated values of the adjustmentspeedsf and g and of the structuralparameters of the productionfunction and long-runfactor demand functions. Ex- pectationsof wages, prices, andoutput are determinedautoregressively, except for the expected wage in the U.S. model, which is determined from the wage equation, assumingthat agents know the Phillips curve and estimate W on the basis of the unemploymentgap observed in the previous period. Significantbreaks in the rate of technical progress, or growthrate of total factorproductivity, are found in the estimates for all countriesafter the firstoil shock and account for much of the slowdown of laborproductivity and potentialoutput, as will be seen below.

Determination of Potential Output

A short-rundisequilibrium is determinedeach period in the simulta- neous solution of the labor marketequations. Firms are not in long-run equilibriumbecause adjustment costs keep them off their planning productionfunction. Neither is there continuousmarket clearing, since

24. Hickmanand Coen, An AnnualGrowth Model; Coen and Hickman,"The Natural GrowthPath. " Robert M. Coen and Bert G. Hickman 143 excess unemployment may exist at the prevailing real wage, either because of deficient aggregate demand or a gap between the full- employment and market wage. As explained earlier, to measure the extent of classical and Keynesian unemployment,it is firstnecessary to determine potential output and the full-employmentreal wage. Our empiricalestimates of these variablesare conceptuallythe same as those derived earlier for a simplified static model, but they also allow for populationgrowth and the endogeneityof laborsupply, for the distinction between employmentand man-hours,for the dynamicsof factor adjust- ments, and for technicalprogress.

THE NATURAL UNEMPLOYMENT RATE The first step is to specify the naturalunemployment rate in order to estimatethe full-employmentlabor supply. We follow MichaelWachter in the method of for the effects of changes in the age-sex composition of the labor force on structuralunemployment.25 In the United States, the demographicshift towardyounger workers from the mid-fiftiesto the mid-seventiesincreased the importanceof age groups with persistentlyhigh unemploymentrates. Moreover, minimumwage legislation may have prevented adjustments in demand favoring un- trainedand lower-skilledyoung workers, and unemploymentinsurance reduced the cost of unemployment so that structural and frictional unemploymentmay have risen among secondary workers, furtherin- creasingtheir alreadyhigh unemploymentrates. Thus some increase in the aggregateunemployment rate consistent with a given degree of labor markettightness and nominalwage pressuresis to be expected. The basic assumptionin estimatingthe naturalrate is that prime-age male workers were largely unaffected by these labor market develop- ments, so that their unemploymentrate in a benchmarkyear can be interpretedas a specific full-employmentunemployment rate that does not change over time and thereforecan be used to isolate that portionof the change in unemploymentrates of the other age-sex groups that is structuralrather than cyclical.

25. MichaelL. Wachter,"The ChangingCyclical Responsiveness of WageInflation," BPEA, 1:1976, pp. 115-59. 144 Brookings Papers on Economic Activity, 1:1987 The naturalunemployment rate for the United States is calculatedas a weightedaverage of the naturalrates for the sixteen age-sex groups:

16 (26) UFt-- UFIt (LF,tILF,) , where UFi is the full-employmentunemployment rate and LFi the full- employmentlabor force in the ith age-sex group. The UFi,are based on the followingregression: (27) Uit = exp[c, + c210gUpt+ c310g(NNIi,INNIt)], where Ui is the actual unemploymentrate in the ith group, U, is the unemploymentrate in the prime-agemale group (forty-fiveto fifty-four in the United States) and the other variablesare as definedearlier. Thus cyclical variationsin the age-sex specificunemployment rates are related to cyclical variationsin Up,whereas structuralshifts in the Ui over time are relatedto the share of the ith groupin the total population.The full- employment unemployment rate for prime-age males, UFp,, is held constantat its 1956level (3.0 percentin the United States), and the other UFi, are estimated by setting U,, = 3.0 in equation 27 and calculating the value of the right-handside. Natural unemployment rates for the other countries are similarly constructed. The prime-agemale group in each country is identifiedas the groupwith both a low mean unemploymentrate and small variance relative to the mean-forty- to forty-nine-year-oldsin Austria, forty- five- to fifty-four-year-oldsin Germany, and thirty-five-to forty-four- year-olds in the United Kingdom.The naturalrate for the prime group is assumed to be constant at the 1965-69 average value of the group's actual unemploymentrate-1.3 percent for the Austriangroup, 0.9 for the Germangroup, and 1.5 for the U.K. group. It is importantto emphasizethat UF is not a nonacceleratinginflation rate of unemployment(NAIRU), since it is not calculatedfrom a Phillips curve by imposingthe nonaccelerationconstraint. It does take account of changes over time in factors affecting structuraland frictionalunem- ployment and the related changes in labor markettightness, but it does not impose the assumptionof a verticallong-run Phillips curve. The naturalunemployment rate equations, togetherwith the partici- pation equations, average hours equation, and identities defininglabor Robert M. Coen and Bert G. Hickman 145 marketaggregates, compose a labor supply system that jointly deter- mines full-employmentvalues of the labor force, employment, unem- ployment,and averagehours, conditionalon the real after-taxconsump- tion wage and demographicvariables. The productof employmentand averagehours gives the full-employmentsupply of man-hours,denoted MHF.

THE NATURAL GROWTH PATH We define potentialgross nationalproduct as that output that would be realized each year if the marketsfor labor and capitalwere continu- ously clearedat the naturalrate of unemployment-that is, as the output along an equilibriumgrowth path.26 A key characteristicof this concept is that potential output is unaffected by deviations of actual output, factor inputs, and real factor prices from their full-employmentvalues. Departures from the natural path imply disequilibriumin the factor markets, as the quantities of capital and labor deviate from their full- employmentlevels, but these temporarydeviations do not affect poten- tial output in subsequent periods, since they can be offset by future changes in investmentand employment. Along the naturalgrowth path of potential output, both labor and capitalare fully employed.Making use firstof the labormarket condition, we definepotential output as the level of outputthat would equate labor at the natural rate of unemployment and full- employmentwage rate. Since the labor demandfunction, equation 24, relates man-hoursto output and relative factor prices, an expression may be derivedfor potentialoutput, conditional on the wage-rentalratio, by substitutingMHF for MH and solving the equationfor output:

(28) XNRPt = A[a/(1 - a)]ct [(W*IQ*)t]oePt MHFJj/f MHFt-(l -Pf" where XNRP is potential output. Since full employmentwould prevail each period along the naturalgrowth path, note thatXNRP depends on MHF in the currentand precedingyear, and hence on all previous years since the path was established, irrespective of whether the economy actuallyoperated at full employmentin the precedingyear.

26. Coen and Hickman,"The NaturalGrowth Path." 146 Brookings Papers on Economic Activity, 1:1987 It remainsto determineW*IQ* = (W*IPI*)[(d+ r)I] - I To do so, we assume that the real product wage grows at the same rate as potential laborproductivity along the naturalpath:27 (29) (WIP)tI(WIP)t_1= (XNRPIMHF)tI(XNRPIMHF)t-l. The real wage in the labor demandfunction is in terms of capital goods prices andthat in the laborsupply equations in termsof consumerprices, but the differentialtrend of consumer and capital goods prices is small enoughthat we ignoreit for presentpurposes, setting (WIP)= (WIPI)in equation 29 and correcting (WIPC)for taxes to derive (WATIPC)in equations 17 and 18. Finally, with real wage expectationsassumed to be realizedalong the naturalgrowth path, (30) (W*IQ*)t (WIPI)t[(d + r)T]1, where the last term is an autonomous component of (W*IQ*),since d and r are exogenous and only changes in T that are unanticipatedand permanentare assumedto affect the equilibriumcapital-labor ratio. (The value of r is constant at 6 percent and may be viewed as a requiredrate of returnon fixed investment.)28 Hence the equilibriumwage-rental ratio increases at the same rate as labor productivityand the real wage along the naturalpath.

27. This assumptionis not only observationallyrealistic but also consistent with the overallstructure of the model. Nominalwages andprices are endogenousin the complete model,but prices are related to unitlabor costs witha constantlong-term markup, implying constantfactor sharesin long-runequilibrium and equalityof the growthrates of the real wage and laborproductivity. 28. In our earlierresearch on the U. S. economy [Coenand Hickman, "Testing Factor Demands for MonetaryInfluences and Technical Change in the Postwar Economy," ResearchMemorandum 241 (Centerfor Researchin EconomicGrowth, Stanford Univer- sity, May 1980)],we tested many alternativemeasures of r involving financialmarket variables:the after-taxlong-term in nominalunits and adjustedfor expected inflation;the correspondingnominal and real after-tax short-terminterest rates; and weighted averagesof after-taxbond yields and two differentmeasures of the returnon equities,again with and without adjustment for expected inflation. None of these constructs performedas well in the estimationof the factordemand equations as the alternativeof an assumedconstant rate of discountof 7 percent(subsequently reduced to 6 percenton the basis of directevidence on real returnsto equity). Ournew estimatesfor Austria,Germany, and the United Kingdomalso incorporatea constantdiscount rate of 6 percent.This assumptionwas againtested againstthe market alternativesof the nominaland real after-taxbond yields and found to lead to superior estimatesof the demandsfor capitaland labor. Robert M. Coen and Bert G. Hickman 147 All the ingredientsare now in place to determinethe full-employment path. Rewritingequation 28 in productivityform as

(31) (XNRPIMHF)t B [(W*IQ*)t]oe' (MHFtIMHF, 1)(' - 1lf, where B = A[(1 - o)/oI]-a, and using equations 17-18, 26-27, and 29-31, and related identities, one can solve simultaneouslyfor the full- employmentvalues of labor productivity,output, labor force, employ- ment, unemployment,hours of work, and the real wage and wage-rental ratio along the naturalgrowth path, for exogenous values of the demo- graphic and policy variables (population, armed forces, employment, and tax parameters).The resulting estimates of the full- employmentwage rate, labor force, employment,and hours are used in the subsequentanalysis of Keynesian and classical unemployment. Capital as well as labor must be fully employed along the natural growthpath. In the standardneoclassical model, a constant fractionof outputis saved and automaticallyinvested; the growthpath depends on the savingrate, and the realwage andreturn on capitaladjust to maintain full employmentof both factors. In contrast, our annualgrowth model includes an explicit investment demand function, equation 25, which determinesactual fixed investment, and need not equal investment ex ante. Our full-employmentequilibrium growth path is based not on a given saving rate, but on a given requiredrate of return on capital.29Equation 25 may thereforebe used to determinethe path of potentialcapital, by setting currentand laggedcapital stock and current output equal to their full-employmentvalues KFt, KFf_ 1, and XNRPt. With the revised equation25 and the identity relatinggross investment and capital stock,

(32) IFt KFt - (1 -d)KFt 1 addedto the earlierequation system, the net and gross fixed investment requiredto sustain the natural growth path are fully determinate. A greaterflow of saving could not be profitablyabsorbed in fixed capital formationunder the given investment conditions, and a smaller flow would be inadequateto attain the requiredrate of capital deepening to equilibratethe capital-laborand wage-rentalratios.

29. See note 28. 148 Brookings Papers on Economic Activity, 1:1987

Decomposing Classical and Keynesian Unemployment

Our initial exposition of the impact of high real wages and deficient effective demandon unemploymentutilized an isoquantdiagram to focus on firms'labor and capitalinput decisions. To allow for an endogenous labor supply and employmentdynamics in the decompositionof unem- ployment, it is more convenient to work with labor supply and demand functions, comparing the actual schedules to their full-employment counterparts.For simplicity, induced variations in average hours are neglected in the theoretical exposition, although they are taken into account in the empiricalestimates. Similarly,we abstractfrom expec- tationalerrors in the theoreticalexposition by assumingperfect foresight on the real wage.30Finally, some complications associated with the carryover effects of lagged disequilibriumin the labor market are postponedfor later discussion.

LABOR SUPPLY AND DEMAND The conceptualframework is illustratedin figure2, in which the real wage rate is measured vertically and the quantity of employment horizontally.The short-runlabor demand function is labeledLD, and its position depends on the quantity of current output and on lagged employmentand other variablesas discussed above. At the currentreal wage and output levels, E persons are employed. The labor supply function, L, is shown as inelastic to the real wage, in view of the small magnitudesof the estimatedelasticities in the variouscountries discussed below. Its position depends on the level and age-sex distributionof the population,and also on the level of E, owing to the discouraged-worker effect on laborforce participation.The numberof unemployedworkers is given by UN = (L - E). The full-employmentlabor force is LF, and EF is the corresponding "full-employment"volume of employment, equal to (LF - UNF), where UNF is the numberof persons who would be unemployedat the

30. The empiricalmeasures are based on the expected real wage. It was shown in Hickman, "Real Wages, AggregateDemand, and Unemployment,"that expectational errorsare normally unimportant determinants of the magnitudeof classicalunemployment in the United States, and the same findingapplies for the other countriesin our sample. Robert M. Coen and Bert G. Hickman 149

Figure 2. Labor Demand and Supply, Actual and Full-Employment

Real wage

LD LDPI

I ~~~~~~~~~~~~~~~~~~~~~~~~~I I ~~~~~~~~~~~~~~~~~~~~~~~~~I I ~~~~~~~~~~~~~~~~~~~~~~~I I ~~~~~~~~~~~~~~~~~~~~~~~I WRF\'| WR ~~~~~~II

E EA EF LLA LF Labor naturalrate of unemploymentUF. Thelabor demand function at potential outputis LDP, and WRFis the real wage rate that would clear the labor market,except for naturalunemployment, if outputwere at its potential level. As discussed above, all these full-employmentfunctions and magnitudesare simultaneouslydetermined in the solutionfor the natural growthpath. Supposenow thatthe realwage were reducedto WRFwhile aggregate demandand output remained unchanged. The level of employmentunder this hypotheticalexperiment would be EA. Thus of the total shortfallof employment (EF - E), an amount (EA - E) is attributable to the wage gap (WR - WRF). The remainder (EF - EA) stems from deficient effective demandfor output. The employment shortfallmay therefore be decomposedinto its wage and demandcomponents: (33) EF - E = (EA - E) + (EF- EA). At the prevailingwage, excess unemploymentexists amountingto UN - UNF. The excess may be decomposed in two ways. First, since (34) UN - UNF = (L - E) - (LF - EF) = (EF - E) - (LF - L), the excess is smaller than the employment shortfallby the amount of "hidden" unemployment(LF - L). The hidden unemploymentis due to the induced withdrawalof potential workers from the labor force 150 Brookings Papers on Economic Activity, 1:1987 because of a perceived lack of opportunitiesat the currentemploy- ment level. Second, the excess unemploymentmay also be factored into a wage componentequal to (UN - UNA) and a demandcomponent given by (UNA - UNF), correspondingto the associatedemployment shortfalls: (35) UN - UNF = (UN - UNA) + (UNA - UNF). The wage componentof equation35 is equal to (36) UN- UNA = (L - E) - (LA - EA) = (EA - E) - (LA - L). Under the hypotheticalwage reduction, the increase of employmentto EA would induce an increase of the labor force to LA. Thus unemploy- ment would fall less than employment rose, owing to the induced reductionof hiddenunemployment.3' The demandcomponent of equation35 equals (37) UNA - UNF= (LA - EA) - (LF- EF) = (EF- EA) - (LF- LA). Thus the demandcomponent of total excess unemploymentconsists of the residualemployment shortfall less the residualvolume of hidden unemployment.The smaller employment shortfallat the reduced real wage would be partly offset by the induced reductionof hidden unem- ployment. This demandcomponent could exist even if the real wage were at the full-employmentlevel. Since it reflects deficientdemand in the product market, it represents the Keynesian component of excess unemploy- ment. Correspondingly,the wage component measures the extent of classical unemploymentdue to an excessive real wage rate.

31. This statementneglects the dependenceof laborsupply on the real wage as well as on employment.To the extent that changes in the real wage affect the size of the labor force, the expression LA - L does not correspond to the usual notion of hidden unemployment;rather, it measures the increase in labor force induced by the rise in employmentplus the increaseor decreasedirectly induced by the declinein the realwage. For the countriesin our study except Austria,the estimatedelasticities, reportedbelow, of laborforce withrespect to realwages arenegative (income effects dominatesubstitution effects), so that for these countriesLA - L will exceed hiddenunemployment, while for Austriait will be smallerthan hiddenunemployment. This qualificationis not important quantitatively,however, because the elasticitiesare all rathersmall in absolutevalue. Robert M. Coen and Bert G. Hickman 151

Figure 3. Carryover Component of Employment Shortfall

Real wage

LD LDB LDPI I

WRF I

E EA EB EF L LA LB LF Labor

EMPLOYMENT DYNAMICS AND CARRYOVER UNEMPLOYMENT It might be thought that the demandcomponent of the employment shortfall(EF - EA) would necessarilybe zero when actualand potential outputwere equal. This is not generallytrue, however, since equalityof actual and potential output does not imply that the actual demand function for labor LD coincides with the full-employment demand schedule LDP. Both schedules depend on lagged employment,but this is measured by EF( - 1) instead of E( - 1) in the case of LDP, since the naturalgrowth path is definedfor a conditionof continuousfull employ- ment. Thus LD would coincide with LDP only if actual and potential outputwere equaland laborwere fully employedin the precedingperiod. Figure 3 illustratesthe situationwhen a shortfallof actual output in this period follows upon excess unemploymentin the precedingperiod, as would occur, for example, if outputand employmentfell below their potentiallevels in period (t - 1) and output recovered only partiallyin period (t). The actual and full-employmentdemand and supply schedules and the associated quantitiesare the same as before. The new scheduleLDB is hypotheticaland shows the demandfor laborthat would exist if actual output were at the potential level, given the actual employmentof the 152 Brookings Papers on Economic Activity, 1:1987 preceding period. The distance (EF - EB) measures the carryover componentof the total employmentshortfall (EF - E). It is the residual shortfallthat would persist even if actual outputand the real wage were both at their potentiallevels in period (t), owing to the drag exerted by the employment shortfall (EF - E) in (t - 1). If carryoverunemployment is recognizedas a separatecategory, the employmentshortfall may be decomposed into three elements: (38) EF-E = (EA-E) + (EB-EA) + (EF-EB). In this formulation,(EB - EA) measuresthe employmentshortfall due to a currentpotential , just as (EA - E) measuresthat due to a currentwage gap. In the illustrative example, the potential output gap is negative (Y < YP)and the wage gap positive (WR > WRF),but the gaps may go either way in principle, and the potential output gaps are frequently positive in the empiricalestimates. The correspondingbreakdown of excess unemploymentis given by (39) UN - UNF = (UN - UNA) + (UNA - UNB) + (UNB - UNF), where UNB = LB - EB, and the other terms were defined earlier. These threefolddecompositions are interestingand meaningful,and empiricalestimates based on equations38 and 39 were presentedfor the United States by Hickman.32The twofold breakdownsgiven by equa- tions 33 and 35 are preferred,however, on the groundthat the contri- bution of deficient aggregatedemand to excess unemploymentshould be measured by the gap between actual output and full-employment output, defined as that output that would be requiredto achieve full employmentof laborif the real wage were at the full-employmentlevel, rather than by the gap between actual and potential output. On this interpretation,the volume of Keynesian unemploymentincludes the carryovercomponent and is measuredby (UNA - UNF) ratherthan (UNA - UNB). A precise measureof the level of full-employmentoutput (XNRF) is given by (40) XNRFt = A[ot/(l - ot)]0ePt [(WFIQFt]o MHFtIfMHt_7S -'f

32. Hickman,"Real Wages, AggregateDemand, and Unemployment." Robert M. Coen and Bert G. Hickman 153 which differs from the expression for potential output in equation 28 only by havinglagged man-hours substituted for laggedfull-employment man-hoursin the last term. Thus XNRF is that output level that would induce firms to hire the full-employment labor supply at the full- employment wage rate, given the level of actual man-hours in the precedingperiod. It mayexceed or fall shortof potentialoutput according to whetheractual man-hours were lower or higherthan full-employment man-hoursin the precedingperiod.33 Note that XNRF is closer to most concepts of potential output than is XNRP, since the formertakes as an initial condition each period the actual state of the labor (and capital) marketin the previous.period. If XNRF were used to define potential output instead of XNRP, no carryover term would be identifiable as an element of the demand component EF - EA.

Measuring the Wage and Employment Gaps

Real wages play a criticalrole in our analysis of the influenceof wage gaps on unemployment and productivity growth. The real after-tax consumptionwage affects laborforce participationand average working hours, whereas the real wage in terms of capitalgoods prices is the key variabledetermining the capital-laborratio. The solutionfor the natural growth path of potential output constrains both real wage rates to in- crease at the same geometric rate as potential man-hourproductivity, before the potentialconsumption wage is correctedfor taxes. An exogenous price shock to the potential investment wage cannot be directly capturedin this framework,however. In the case of the first oil shock, for example, the unanticipatedexplosion of import prices (PM)raised the prices of investmentgoods (P1)sharply relative to money wages (W)in the United States, leadingto an abruptdrop in the ratio of the real wage (WPI)to laborproductivity (PROD) that persistedinto the early eighties, as shown in figure 4. For given values of the other

33. A similar distinction between full-employmentoutput and potential output is discussed in Hickmanand Coen, "An AnnualGrowth Model," pp. 17-19, but without relatingtheir definitions to the conceptof the naturalgrowth path. The latterconcept dates fromCoen and Hickman,"The NaturalGrowth Path." 154 Brookings Papers on Economic Activity, 1:1987

Figure 4. Ratio of Real Wages to Productivity, United States, United Kingdom, Germany, and Austria, 1966-84a Ratio of real wages to productivity 0.76 United States

0.74 -

0.72-

0.70 -

0.68

0.66 r 1968 1970 1972 1974 1976 1978 1980 1982 1984

Ratio of real wages to productivity 0.74 United Kingdom

0.72

0.70

0.68 -

0.66

0.64 . . . 1968 1970 1972 1974 1976 1978 1980 1982 1984

Source: Authors' calculations based on data from the following sources: for the United States, U.S. Department of Labor, Bureau of Labor Statistics; for Austria, Austrian Institute for Economic Research; for Germany and the United Kingdom, Organization for Economic Cooperation and Development, Labor Force Statistics, various issues, and additional unpublished data from the OECD. Robert M. Coen and Bert G. Hickman 155

Ratio of real wages to productivity 0.68 Germany

0.66-

0.64 -

0.62

0.60 . 1968 1970 1972 1974 1976 1978 1980 1982 1984

Ratio of real wages to productivity 0.66 Austria

0.60 -

0.58

0.56 ...... 1968 1970 1972 1974 1976 1978 1980 1982 1984

a. Ratio of real wage rate in terms of investment goods prices to actual labor productivity. For the United States, the wage pertains to all workers, including the self-employed. For Austria, Germany, and the United Kingdom, the wage includes employees only. 156 Brookings Papers on Economic Activity, 1:1987 components of rental price, the exogenous reduction of the real wage decreased the wage-rentalratio (equation30). An exogenous downshift of 7 percentin the real wage was accordinglyimposed in the solutionfor the naturalgrowth path during 1974-75, resulting in a corresponding once-for-allreduction in the desiredcapital-labor ratio and the time path of potential output. Thus part of the deceleration of potential output growth during the subsequent five years or so reflects the gradual transition to a lower growth path. Without this relative price shock adjustment,potential productivity would not respondto the importprice shock, and the wage gap would be understated.34 Another, equivalent, way of understandingwhy the potential path must be adjustedfor the relative price shock is to examine its effect on the rate of returnon capital. As shown earlier,in footnote 17, the rate of returncan be expressed as R = oa(PIPI)( YIXK)- d. In the United States, the energy shock induceda lastingincrease in the price of capitalgoods, Pl, relativeto the price of finaloutput, P, of about7 percent. To maintain the pre-shockrequired rate of returnof r, the marginalproduct of capital, cx(Y/K),must thereforerise, and this requiresa decrease in the capital- laborratio and a correspondingonce-for-all drop of the potentialoutput path for the given potentiallabor path.35 The same sort of behavior is observable in figure 4 for the United Kingdom, except that the importprice explosion began in 1973instead of 1974.Just as in the United States, the real wage path drops discontin- uously as a result of the , and the wage-rental ratio is adjusteddownward in the potentialsolution.

34. The effect of this price-inducedincrease in the relativecost of capitalservices on actual productivityis capturedautomatically through the observedwage-rental argument in the estimatedfactor demandsystem. For furtherdiscussion of the impact of energy shocks as measuredin the model, see RobertM. Coen and Bert G. Hickman, "Energy Shocksand Macroeconomic Activity: Results from the Hickman-CoenModel" (EnergyModeling Forum, Stanford University, November 1983). Other exogenous shocks may also affectthe factorprice ratio and potential and actual output. Thus the depreciation incentives in the 1981tax legislationare estimatedto have reducedthe rental-wageratio sufficientlyto increasethe level of potentialoutput, but not the long-rungrowth rate, by about 1 percent in the 1980s. See Robert M. Coen and Bert G. Hickman, ", FederalDeficits, and U.S. Growthin the 1980s,"National TaxJournal, vol. 3 (March19, 1984),pp. 89-104. 35. A relativeprice shock cannotaffect total factor productivity, which has nothingto do with factor substitution,but it may alterthe accompanyinglevel of laborproductivity by inducinga movementalong the productionfunction to a differentcapital-labor ratio- in this case, to one with less capitaland outputper workerand a lower potentialoutput path. Robert M. Coen and Bert G. Hickman 157 The reactionof the realwage to the oil shock was differentin Germany andAustria. The increasein importprices was considerablysmaller than it was in the United States and United Kingdom, and nominal wages increasedmore than investmentgoods prices. As a result, the real wage rose relative to productivityin both countries in the aftermathof the shock and did not recede muchuntil several years had passed, as shown in figure4. There is no direct evidence here of an unexpected shock to the potential path such as occurred in the United States and United Kingdom,and no adjustmentis made to the potentialwage-rental ratio as determinedby the productivitytrend. This means that the wage gap may be overstatedin these countriesto the extent that agents may have viewed part of the rise in the real wage as permanentlyaffecting the growthpath. The second oil shock was much smallerin relative terms as indexed by the importprice increases during1979-80. The United Kingdomwas by then an oil exporterand the other countries were less dependenton importedoil than before. Finally, the dollar appreciated one-third between 1981 and 1984, driving down the real price of U.S. imports and investment goods by one-fifth and one-tenth, respectively, with the result that the real investment wage far outpaced the growth of productivity(figure 4). A correspondingadjustment was phased into the potentialreal investment wage and wage-rentalratio duringthose years in allowance for the real price shock. Estimates are required of the full-employment and hypothetical magnitudesin figure 2. The full-employmentestimates have already been described. The hypothetical values of employment, unemploy- ment, and labor force were obtained by simulationmethods, using the labor marketblocs of the models. To calculateEA and LA, the demand and supply functions for labor were solved simultaneously,using the actual values for output and other shift variables external to the labor market, and the potential or full-employmentvalues of the real wage rates entering labor demand and supply. The various shortfalls were then calculated from these solutions and the actual historical data on employment,unemployment, and laborforce.36

36. In orderto purgethe calculatedshortfalls of stochasticerrors, the hypotheticalor counterfactualsimulations were based on a simultaneoustracking solution of the labor marketblocs, in which the single-equationresiduals had been added to the stochastic equationsfor the endogenousvariables. NM Ox Ox r, - n "! M " CII " nc > c~~~~~~~~~tfi)v r- clo .!

Cl _l cdlc~00O 0 U * * o t 'It ^ N un aN tr 0N .m n . ~~N~~~ ~ tr) tr) c

hN -^n 00 chc

c W- -T 0 -

_~~~~~~~~~~~~~~~~~~~~~~~Wun VR- o~~~~~~~~~~~~~~~~~~~~~cONo 00xt lZ "I CZ r- I) r- "It _ ^n ^_

N r t o No N N o o o o. o tC~~~~~~~aN_ X ^ *

O hunNN O >?_ otC O cd

_ _ ~~~~~~~~~~~~~~~~~~~~~~~~~CZ

lZ "IN ht "t O cn ^ O <

el M, r, 09r,N n-: in N^ cn W) c. ON _"Ii ON x? t "t O CII CII O C

_Z aN CZm

O-N W) W) W) O 09^? .O O 000t h t "IOt CII CII cd

ON r- n _l cl 09 _ _ v o oo o o o o o X ? ^0~~~~~g ?n clt r-_* .) n qC

lZ 0 "I lZ aN r- r- O a, lZ a N"I = >O

00 r- ot "I O O O Q Qc_ fi_O O -- -. X*

00 "OUOI t X : s fi_ O O -- - cdZ

00CI fi _ _~~~~~~~0cl~09 ,I 09 NC 00 "It aNo "It coI CII W) - u" W?-!_ > X B -N > ^ o ^ o I m~~~~~~~~~~~~~~Itmo ?

r- 0 a ^N ah^;N CII W) 'I _ -cd 0 0

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00 "I "I?t N)N^O X s l' C Qp=

X | Q O r- ON Y< 0 O < 0QO YnQn Robert M. Coen and Bert G. Hickman 159 These are partial equilibriumresults. No allowance is made for a feedbackfrom the alteredvalues of labor marketvariables to aggregate demand and output. The procedure is appropriatefor measuringthe wage and demandcomponents of unemployment,but not for investigat- ing the consequences of an exogenous reductionof real wage rates for the economy as a whole.

Output, Unemployment, and Real Wage History

It is useful to observe the historyof actualand potential gross national product, unemployment,and real wages before examining the unem- ployment decompositions. Wage gaps are reportedfor both the invest- ment and consumptionconcepts of the real wage, but it is the former that is meantby an unmodifiedreference to the real wage gap. As shownin table 1, the U.S. economy seldomoperated at its potential level during 1961-84, exhibitinginstead varying periods of under- and overutilizationas measured by the ratio of actual to potential output. The doldrumsof the early sixties were succeeded by the Vietnamera of low unemploymentand high utilization.The economy did not stray far from potential during 1970-72, but utilization exceeded potential by 2 percent in 1973, before declining in 1974-75 to a low of 96 percent followingthe oil shock. The subsequentrecovery carriedthe utilization rate to 103percent during1978-79, before it againdeclined to a twenty- year low of 92 percent in 1983,to be followed by a vigorous but incom- plete recovery in 1984. Duringthe 1960s,unemployment exceeded the naturalrate whenever actualoutput fell below potential, and vice versa. This outcome is not a necessary one under the Hickman-Coenconcept of the naturalgrowth path of potential output, as it would be in constructs that assume competitivemarkets for goods andservices eitherexplicitly or implicitly. Under competitive conditions, if actual unemploymentis at the natural rate, actual output must necessarily be at the full-employmentlevel, because competitive firms choose what output to supply, given wages and prices, at the same time as they choose how much labor to employ. The outputresulting from a clearedlabor market is thereforeby definition at the full-employmentlevel. With price-setting firms and imperfect markets, however, labor demand is conditional on output, which is o~~~~~~~~~~~~cn (C en 00 4 ON r-bbbo a- C) a-, 0 ON ON cq a-,o

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0 aN io>8 8sW ~ ?vv , S z j ., S o :Q d DQ Wo Robert M. Coen and Bert G. Hickman 161 demand-determinedin productmarkets. Unemploymentmay therefore exceed the naturalrate even with output at its potentiallevel, if the real wage is above the level that would prevailif the labor marketwere to be clearedat potentialGNP, or if carryoverunemployment exists because of a precedingshortfall. Such excess unemployment actually occurred with the economy slightly above potential in 1977 and in 1980 because the real wage gap (WR/WRF)was positive and large, as shown in the third and fourth panels of the table.37Of course, effective demandmay also occasionally offset the adverse effects of a large wage gap, as it did in 1978-79, when unemploymentwas reducedto the naturallevel by higheffective demand as reflectedin a utilizationrate of 103percent. The wage gap was small or negative duringthe early 1960s, so that classical unemploymentcould not have been an importantproblem. The wage gap rose to successively higherplateaus duringthe War years and in the mid-1970s and early 1980s, however, increasing its unemploymentimpact. Similar capsule histories of output, unemployment, and real wage gaps are presentedfor Germanyand Austriain tables 2 and 3. Germany grew rather steadily and operated close to potential output and the naturalemployment rate during most of 1966-73, except for the mild of 1967and the subsequentoverheating that culminatedin the wage explosion of 1970. Growth in Austria was even steadier during 1966-73, unemploymentwas never excessive, and output did not rise much above potentialuntil the final year. Real wages were moderately high in Germanyduring this period, parallelingthe contemporaryexpe- rience in the United States, but in Austria they did not deviate much from the potentiallevel. The unemployment situation deteriorated markedly in Germany followingthe energy shock, with the actual rate risingfrom 1.0 percent in 1973to 8.2 percentin 1984as the naturalrate scarcely increased. The real wage gap increased sharplyduring 1973-75 and trendeddownward graduallythereafter, with the economy operatingbelow potential most of the time. In contrast, Austriakept unemploymentunder control until 1980by offsetting the real wage gaps that emerged after the oil shock with positive output gaps. Beginningin 1981, however, Austrianexpe- 37. Carryoverunemployment also contributedto the excess, but it was less important thanthe realwage gap. ) C) 0 00 % (N 00 kf en C) I% 0

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0o 0o 00 00 t } t}

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W? ~~~~~~fv _; ?v z< nW Robert M. Coen and Bert G. Hickman 163 rience followed the German pattern: underutilizationof productive potential,rising unemployment, and a decliningwage gap. The United Kingdomexperienced moderate excess unemployment during1967-74, owing to a substantialwage gap that nullifiedgenerally high levels of potential utilization(table 4). The wage gap increased 50 percent during 1975-76, drifteddownward during the remainderof the decade, and rose again in the eighties. Unemployment rose from 2-3 percentin 1967-75to about5 percentin 1976-79and climbed dramatically thereafter.

Classical and Keynesian Components of Unemployment

The proximatesources of excess unemploymentin the U. S. economy are quantifiedin table 5, which reportsthe measuresand decompositions that were definedin equations33-37. The naturallevel of unemploymentrose from about 3 millionworkers in 1961to more than 6 millionin the last half of the 1970s.The estimated excess of actualover naturalunemployment was positive in the firsthalf and negative in the second half of the 1960s.Excess unemploymentwas also negative during1972-74 and in 1979,but it was positive in 1975-78 and again in 1980-84. The worst years by far were 1982-83, when the excess over naturalunemployment is estimatedat 4.5 millionpersons. Employmentwas below its naturallevel (the shortfallwas positive) during all but the Vietnam War years 1966-69. That measure of the unemploymentproblem, however, can be seriously misleadingbecause of hiddenunemployment. As shown in the second panel, the volume of hidden unemploymentis often substantial, so that eliminationof the employment shortfallwould reduce unemploymentby a considerably smalleramount. The employment shortfall is factored into its wage and demand components in the third panel, and excess unemploymentis similarly decomposed in the final panel. The results confirm that the wage componentof unemployment,which was negligiblein the early 1960s, rose moderatelyduring the Vietnam years and the early 1970s and hit new heights thereafter.Between 1965 and 1974high effective demand more than offset the moderate wage gaps, and excess unemployment C00 en 00 e00I enO ,N C 000 0 00 0-1 ON e 0 cfi Ite 00 CAm =

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r- 00 \C r- O m \C r- r O b Q W)00 It 00 00 OIt 0 0 00 U Ch I b b ~~~~~~~~Itl (1 -o 00 ^ ??

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^~~~~~~~~~0"I m o 0 "It m It r- C1 00 0 o

o <

00\ t 00 o 00 0 WI 00 -? enoo N _~~.ooten - "t "I CN en o NI C-, -C1 r- O C Z ; 06 C o ; a, O; 4 cl C 06 O CI Z: r- r- -, r- \c a- \CN ^ t O _ Ch O t N~~~~~~~~~0O C? 00 \0 0 w l ._C~ol l l l l Cl l w~~~~~~~~~~~~:) q O Q~~~~~~~~~~~~1I0?t or- 0 0 00000o 0 > _ ^ o ^ X ^ t t t E ~~~~~~~~~~~~~~~o^ . \C r O r 00 00 zlO 06 o ^OX

Q oIO 00 - ?. ?. \?. I?." O m \ . N t _ ~~~~~~~~~"tC1 C1 en (, - > Cht ^N~~~~~\ O \C \Oc u~~~~~~~~~een en <, "It r- I- m4\ _ U <> te) ce)Nco\>Nb- u ca s 11oo > o 11oo @ > > @ > oo U oo ^ < 4 Robert M. Coen and Bert G. Hickman 167 was negative in all years save one. After 1974,however, unemployment exceeded the naturallevel in most years. Duringthis periodof chronically high unemployment,the wage or classical componentwas the dominant factor in 1977and 1980, whereas the demandor Keynesian component was the principaldepressant during 1975-76 and 1981-84. Finally, high effective demand neutralized the effects of high real wages during 1978-79, as unemploymentfell to the naturallevel for the only period between 1974and 1984. The componentsof unemploymentin Germanyare presentedin table 6. Unemploymentwas below the naturallevel duringmost years in the later sixties and early seventies, but a chronicpositive gap developed in 1974-82.Hidden unemployment, though sizable, was a relativelysmaller component of excess unemploymentthan it was in the United States, because of the low employmentelasticity of laborforce participationin Germany(0.17 as comparedwith 0.37 in the mid-seventiesin the United States). Classical unemploymentincreased markedlyin the mid-seven- ties, but the Keynesian componentwas relativelymore importanteven in these years, and it accountedfor virtuallyall of the poor employment performanceof 1981-84. Unlike the United States and Germany,Austria did not experience chronic unemploymentafter the OPEC oil shock, because of offset- ting classical and Keynesian components (see table 7). When excess unemploymentdid finally appear in 1981-84, it was associated with a demand shortfall rather than a wage gap. Hidden unemploymentis substantialin Austria, owing to the largest employment elasticity of labor force participationin the group of four countries (0.48), and was negativemore often thannot, since the employmentshortfall was usually negative. Excess unemploymentin the United Kingdom,which was moderate in 1967-75, rose somewhat in 1976-80 and stayed at markedlyhigher levels thereafter (table 8). The unemploymentof the early years was classical but the balance shifted towardthe Keynesian componentafter the first energy shock, albeit with sizable contributionsin most years fromthe continuingwage gap. The bulk of the rise duringthe eighties is attributableto a demand shortfall,however, just as it is in Austria and Germany.Hidden unemploymentis relatively moderate in the United Kingdom,where the employmentelasticity of the laborforce is estimated to be 0.22. 00 CAIN 00 if) r- W) C- 00 00 en .~ .; .; .~ .r .~ . 0. . . $ o o o o mm m oo xooC " o ^ xo xot btNCA It b xo t Nt^~el, rN o 'I CA W) 'I en 'I CA - W)

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Key Determinants of the Classical Component

The magnitudeof the wage component of the employmentshortfall depends on the wage elasticity of labor demandas well as on the size of the wage gap. Given a Cobb-Douglas technology and assuming that adjustmentcosts keep firms off the long-runproduction function, the short-runelasticity of man-hourinput with respect to the real wage rate, holding constant other components of the wage-rental ratio, is the negative of the product of the capital coefficient in the production function (a) and the adjustmentspeed of labor input (f). For the United States, the estimated values of these parametersfrom equation 24 are 0.25 and 0.65, yielding an estimated wage elasticity for man-hoursof - 0. 16.The correspondingfigures are 0.30, 0.65, and - 0. l9forGermany; 0.32, 0.58, and -0.18 for Austria; and 0.24, 0.91, and -0.22 for the United Kingdom. These small elasticities clearly restrict the scope of wage gaps as a cause of unemploymentin the various countries, but large wage gaps may still account for substantialunemployment, as we have seen. An additionalcomplication is introducedby the endogenousresponse of average working hours to wage changes. In all four countries, the partialwage elasticityof averagehours is negative,indicating dominance of the income over the substitutioneffect, and rangesfrom - 0.04 in the United States to - 0.10 in Germany, - 0.17 in Austria,and - 0.19 in the United Kingdom. Thus the direct result of a real wage reduction is to increase average hours, partly nullifying the favorable impact of in- creased man-hourdemand on employment. In the model of Germany,the response of average hours is confined to the direct impactof the wage reduction,so that the total employment elasticity is the difference between the elasticities for man-hoursand averagehours, or - 0.09.38 Althoughthe partialelasticities for the other countriesare also negativeand thereforeoperate to weaken the employ- ment response to a wage change, the total response of average hours also includes the effects of induced changes in other employment or labor force variablesand cannot be directly estimated from the partial

38. The consumptionwage gap in Germanywas negativein 1982-84,so thatreversion to the full-employmentconsumption wage reduces average hours and reinforces the favorableimpact of the reductionin the investmentwage on employment(tables 2 and 6). Robert M. Coen and Bert G. Hickman 171 elasticities. The total response of averagehours is smallin any event for the United States, but it appearsto be substantialfor the othercountries. Manyempirical analyses of the effects of realwages on unemployment neglect the role of induced variations in average hours by measuring laborinput by employmentrather than man-hours in productionor labor demand functions or in reduced-formequations for employment or unemployment. Our results suggest that this is a serious omission in view of the offsettingeffects of wage changes on man-hoursand average hours of work. The contributionof a wage gap to an employmentshortfall depends only on the elasticity of demandfor labor input and the overall respon- siveness of average hours, whereas the wage component of excess unemploymentis additionallyaffected by the induced labor force re- sponse to the hypotheticalwage change. The small wage elasticities in the labor force participationequations for Germany and the United States ( - 0.04 and - 0.01) severely constrainthe direct impact of wage reductionson the labor force, but in the United Kingdomand Austria, the wage elasticities are large enough (-0.07 and 0.11) to exert a moderate effect on the labor force. As noted above, moreover, the employment elasticities are substantialin all the countries, so that a considerable portion of the employment gain from a wage reduction would be nullifiedby an additionalinflux to the laborforce.

Potential and Full-EmploymentOutput

In this section we compare the empiricalmeasures of potential and full-employmentoutput, as calculatedfrom equations 28 and40, in tables 9-12. Also includedare utilizationindexes measuringthe ratio of actual output to potential and full-employmentoutput, plus the ratio of full- employmentto potentialoutput. The utilizationrate of full-employment output is a direct indicatorof the amount of output change that would eliminatethe Keynesian component of unemploymentin a given year. The potentialutilization rate is the preferredmeasure of overallresource utilization,since it shows the extent to which an economy adheresto its naturalgrowth path embodyingfull employmentof labor and capital at normalintensities. In the United States, the difference between potential and full- n 00 e N ena 'ICeN1 00 O

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More on the Wage Gap and Classical Unemployment

The pioneering wage-gap analysis of Sachs and Bruno attached considerableimportance to the emergencein the 1970sof largedisparities between the real wage "warranted" by full-employment productivity and the realized product wage in many industrialized countries: In the late 1960sand early 1970s,a real wage explosion (particularlyin and )caused a major shift of income distributionaway from profits and toward labor. Even before the oil shocks, therefore, many OECD countries faced a major problem of declining profitabilityand slowing growth. In the second phase real wages did not decelerate (outside of the United States) to makeroom for the rawmaterial price increases, so the profitsqueeze intensified. In the thirdphase low profitabilityand risingunemployment slowed the rate of capital accumulationand productivitygrowth. Real wage increases were re- duced, but so too was productivitygrowth, with the result that the excess of wages over full-employmentproductivity persisted into the early 1980s.39 Thus some, but by no means all, unemploymentwas induced from the supply side by price shocks and excessive labor costs: We have suggested that the sharp increases in unemploymentduring 1973-75 and 1979-82 are mostly demand-inducedand resulted from the applicationof tight monetarypolicies to the supply shocks and high inflationin 1972-73 and 1979-80.The steady rise in unemploymentduring 1975-79 in most of the OECD,

39. Bruno and Sachs, Economics of Worldwide Stagflation, p. 167. See also Jeffrey D. Sachs, "Wages, Profits, and MacroeconomicAdjustment: A ComparativeStudy," BPEA, 2:1979, pp. 269-319. Robert M. Coen and Bert G. Hickman 177 Table 13. Comparisonof Real Wage Gap Estimates,United States, Germany, and the UnitedKingdom, Selected Years, 1965-83

Estimate 1965a 1970 1973 1976 1979 1981 1982 1983

United States Bruno-Sachs 1 1.2 -1.3 3.1 0.6 4.0 5.0 5.3 4.9 Bruno-Sachs 2 0.2 0.1 6.0 2.9 6.8 8.1 8.6 8.4 Coen-Hickman 1 2.0 7.1 6.2 7.5 11.9 11.2 11.2 11.2 Coen-Hickman 2 1.2 8.4 6.9 8.3 12.7 10.7 11.2 11.0 Germany Bruno-Sachs 1 1.7 1.9 8.0 14.0 14.6 17.1 13.3 9.6 Bruno-Sachs 2 2.0 1.5 7.2 13.0 15.3 19.1 15.9 12.9 Coen-Hickman 1 2.6 2.8 8.0 14.7 9.0 4.1 2.6 1.4 Coen-Hickman 2 1.0 3.3 6.9 9.8 8.6 4.0 -0.2 -2.4 United Kingdom Bruno-Sachs 1 -1.5 1.5 3.1 8.1 9.3 14.3 13.9 13.9 Bruno-Sachs 2 -2.0 2.2 4.6 11.0 16.4 24.1 25.0 26.4 Coen-Hickman 1 4.9 9.6 9.2 13.3 7.0 10.8 13.6 17.7 Coen-Hickman 2 2.7 4.4 8.4 11.4 7.4 12.4 8.7 10.6 Sources: Bruno-Sachsestimates of the real value-addedwage gap in manufacturingare from MichaelBruno, "AggregateSupply and DemandFactors in OECDUnemployment: An Update,"Economica, vol. 53 (Supplement, 1986),pp. S35-S52. Variant1 assumesthat the wage gap was zero on averageduring 1965-69 and uses the average growthrate of labor productivityduring 1960-73 and 1973-85as the full-employmenttrend. Variant2 correctsfor the effect of the unemploymentlevel and its changeson full-employmentproductivity growth using a regressionof realizedproductivity on a time trend(with a trendbreak in 1975)and the unemploymentvariables. Coen-Hickman estimatesof the real wage gap in termsof investmentgoods (variant1) and consumptiongoods (variant2) are from tables 1, 2, and 4. a. 1966for Germanyand the UnitedKingdom in the Coen-Hickmanestimates. however, shouldbe attributedto the fact thatreal wages remainedabove market- clearinglevels in most (but probablynot in the United States).40 These capsule summariesare based on an impressivearray of theoretical andempirical analyses, fromamong which we can commentonly on two or three issues relatedto our own estimates.

WAGE GAP ESTIMATES Table 13 compares our estimates with those of Bruno and Sachs as updatedthrough 1983.41The following points should be borne in mind when examiningthe table. -The Bruno-Sachsestimates are for the real value-addedwage in manufacturing;our estimates, for the economywide real wage in terms of capitalgoods prices.

40. Bruno and Sachs, Economics of Worldwide Stagflation, p. 171. 41. MichaelBruno, "AggregateSupply and Demand Factors in OECD Unemploy- ment:An Update,"Economica, vol. 53 (Supplement,1986), pp. S35-S52. 178 Brookings Papers on Economic Activity, 1:1987 The Bruno-Sachsmeasures are conceptuallybased on the assump- tion of output marketclearing with competitive firms operatingon the notional labor demand function, equation 2, whereas ours assume imperfectcompetition and the conditionallabor demand function, equa- tion 6. -Both approachesassume a Cobb-Douglastechnology, with the full- employmentreal wage following the trend of full-employmentproduc- tivity. They differ substantially,however, in the methodof determining the productivitytrend, and Bruno and Sachs offer two variants of the productivitytrend and wage gap series. The firstof theirmeasures shown in the table assumes that the wage gap was zero on average during 1965-69and takes the averagegrowth rate of measuredlaborproductivity during1960-73 and 1973-85to representthe respectivefull-employment trend. In the second variant-the adjustedwage gaps-they attemptto correctfor the effect of the unemploymentlevel and its changes on full- employmentproductivity growth using an ad hoc regressionof realized productivityon time, with a trendbreak in 1975,and the unemployment variables. In our measures the potential productivitypath is endoge- nously determinedby a structuraleconometric model of labor supply and demand, where the latter incorporatesthe parametersof the pro- duction function and the adjustment process. The wage gap is not normalizedto zero in the late sixties because our frameworkdoes not assume that the existence of approximatelyfull employmentnecessarily implies that the labor marketis clearingat the observed wage rate. Accordingto both measures, the real wage explosion before the first energy shock was pronouncedin Germany.Bruno and Sachs's finding thatthe wage gap also increasedsubstantially in the United States during 1970-73is puzzlingand probablyreflects a sizable underestimateof the gapfor 1970,owing to theirnormalizing assumption that the labormarket was in equilibriumduring 1965-69 despite the overheatingassociated with the Vietnam War. The estimated wage gap in our annual growth model, in contrast, was ratherlarge in 1970and actuallyfell duringthe next three years of higherunemployment. The U.K. gap in our estimates was also much higherin 1970-73than duringthe late sixties. Bruno and Sachs's finding of a sharp increase in the wage gap in Germanyand the United Kingdombetween 1973and 1976in reactionto the first oil shock is confirmedin our measures. For the United States, our estimatedgap increases somewhatduring this period, whereas their Robert M. Coen and Bert G. Hickman 179 figure declines substantially.The increase reflects our downward ad- justmentof the potentialpath of laborproductivity in response to the oil shock as describedabove. Both studies show a decline in the Germanwage gap duringthe early 1980s. The decline began much earlierin our estimates, however, with the gap narrowinggradually in 1976-79 and rapidlythereafter. By 1983 the gap had virtuallydisappeared in our measure but was still large in the Bruno-Sachsmeasures. The wage gap for the United States rises duringthe early eighties in the Bruno-Sachsestimates. The gap decreases slightlyafter 1979in our estimates, but even so it remainsabove the Bruno-Sachsestimates. In our estimates the wage gap for the United Kingdom decreases during 1976-81 and rises again in 1981-83, whereas the Bruno-Sachs measuresrise steadilyafter 1976.By 1983their two variantsbracket our estimate.

WAGE GAPS AND LABOR DEMAND The initial theoretical derivations by Bruno and Sachs relating the real wage gap to the employment gap are explicitly based on the unconstrainedcompetitive model, implying that all unemploymentis classical and that eliminatingthe wage gap would restore full employ- ment.42However, they do not in fact use the competitivedemand curve for labor to evaluate the employmenteffects of real wages, since they share our distrust of the restrictive assumptions of the competitive model, namely, that firmsare generallynot demand-constrainedand are usually on their production frontiers and notional supply schedules. Instead, they "modify the conventional demand curve for labor by assuminggradual adjustment as well as a short-runrole for aggregate demandfactors. " 43Thus their reduced-formequations for labor input in manufacturing,although conditional on capital stock, also include demandvariables along with the real wage rate. Similarly,their reduced- form equationsfor aggregateunemployment include the adjustedwage gaps estimated for manufacturingas proxies for the corresponding

42. Bruno and Sachs, Economics of Worldwide Stagflation, chap. 9; Bruno, "Aggre- gate Supplyand DemandFactors." 43. Bruno," and DemandFactors," p. S45. 180 Brookings Papers on Economic Activity, 1:1987 aggregativemeasures, along with real money balances, the government deficit, and world tradeas demandvariables, but omit capital stock.44 It is noteworthythat their unemploymentregressions attribute much less importance to the wage gap than is implied by the competitive theory. Recall that, under a Cobb-Douglastechnology, the elasticity of employment with respect to the real wage for a competitive, - maximizingfirm in the shortrun is the reciprocalof the capitalelasticity in the productionfunction, or about 3 or 4 for realistic values of the capital elasticity. In interpretingthe results of a pooled unemployment regression for eight countries that is representativeof their findings, Bruno reports that for each 1 percent rise or fall in the wage gap, the unemploymentrate rises or falls by 0. 15percent within two years.45This short-runelasticity of about 0.15 resembles our estimates and is far below the value of 3 or 4 that one would predict from the competitive model of a firm's labor demand decision under unconstrainedprofit maximization. Accordingto these recent findingsof Bruno, there was essentially no wage-relatedunemployment in the United States during 1970-82; de- mandand wage factorswere aboutequally prominent in Germanyduring the same period, but the role of demandwas risingtoward the end; and the wage gap was the dominant influence in the United Kingdom throughoutthe period, but with demand restraintassuming increasing importanceafter 1978. Our own estimates give much less weight to the wage factorin Germanyand the United Kingdom,but agreethat demand constraints became relatively more important in the 1980s in both countries. On the other hand, the wage gap plays a larger, though still subsidiary,role in our analysis of U.S. unemployment.

Investment Demand and Productivity Part of the Bruno-Sachsthesis is that the supply-inducedwage gaps of the first half of the seventies led to a thirdphase of low profitability and rising unemploymentthat slowed the rate of and productivitygrowth, thereby tendingto perpetuatethe wage gaps.

44. See Bruno, "AggregateSupply and Demand Factors." This specificationis a modification of the one appearing in Bruno and Sachs, Economics of Worldwide Stagflation, chap. 10. 45. Bruno, "AggregateSupply and DemandFactors," p. S48. Robert M. Coen and Bert G. Hickman 181 In 1986 Bruno estimated rate-of-profitand investment equations for eight countriesthat led to the generalconclusion that outputcontraction from the demandside was the dominantfactor in the profitsqueeze and investmentcontraction, with high real wages playingonly a small direct role in the reductionof capitalformation. Bruno's findings are in general accordwith our own, but our interpretationis ratherdifferent, especially as regardsthe relationshipbetween investmentand productivity growth. Ourinvestment demand function, equation25, depends on expected rather than realized profitabilityand is derived jointly with the labor demandequation on the assumptionof cost minimization.Investment thereforedepends on the wage-rentalratio, and hence on the real wage rate in terms of investment goods, as well as on output and technical progress. Along the naturalgrowth path, the level of man-hourproductivity (equation31) is governed by the rate of technical progress (growthrate of total factor productivity);the equilibriumcapital-labor ratio, which in turndepends on the equilibriumwage-rental ratio; and the growthrate of full-employmentman-hours. As we have shown elsewhere, the last term is an implicit measure of the intensity of use of employed man- hours.46The contributions of these three components to potential productivitygrowth before and after 1973,as calculatedfrom our factor demandestimates, are shown in the firstfour columns of table 14. The rate of technicalprogress decelerated after the early seventies in all the countriesin our sample, as did potentialproductivity growth. The rate of growth of the full-employmentreal wage also decreased in line with the slowdown in productivitygrowth (equation29), thereby mod- eratingthe secularincrease in the wage-rentalratio, reducingthe rate of capital deepening, and further slowing productivitygrowth. Thus the slowdown in technicalprogress induced a decline in capitaldeepening, andhence in the net investmentrequirement to sustainthe naturalgrowth path of output. The causationruns from reducedproductivity growth to reducedinvestment, ratherthan the reverse. In the cases of the United Kingdomand United States, real investmentdemand was also reduced by the unexpected exogenous drop in the investment wage and wage- rentalratio resulting from the firstoil shock. Table 15 compares the actual and potential shares of investment in

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Table 15. Investment Shares of Gross National Product, United States, 1956-84, and of , Germany, Austria, and the United Kingdom, 1966-84 Percent

Naturala Realizedb Period Net Gr-oss Net Gross United States 1956-68 2.40 9.50 2.42 9.58 1968-73 2.37 10.01 2.60 10.49 1973-84 1.99 10.29 2.09 10.96 Germany 1966-73 10.29 22.17 11.69 23.78 1973-84 7.78 20.40 7.07 21.37 Austria 1966-72 10.02 25.2 10.80 25.95 1972-84 7.90 23.78 8.46 24.87 United Kingdom 1966-73 9.89 18.91 11.26 20.50 1973-84 7.15 17.24 6.58 17.98

Sources: Authors' calculations with data cited in tables 1-4. a. See text description accompanying equation 32. b. For the United States, unpublished estimates of private, nonresidential net capital in constant prices were prepared by the Bureau of Economic Analysis; for Germany and the United Kingdom, benchmark estimates of real net capital, including residential and government capital, from OECD, Flows and of Fixed Capital (OECD, 1983); for Austria, estimate was derived from a study of gross capital stocks by Franz Hahn and Ingo Schmoranz, "Schaetzung des oesterreichischen Kapitalstocks nach Wirtschaftstbereichen," Monatsberichte, Austrian Institute for Economic Research, vol. 56 (1983), pp. 40-52. Equation 32 in the text was applied recursively to generate capital stock series from the benchmarks, using real gross investment expenditures from the . aggregateoutput. For the United States and Austriathe realized shares are larger, so that actual exceeded the investment requirementsfor potential output during the seventies and eighties.47 The same was true of Germanyand the United Kingdomfor most of the period. The upshot is that in 1984the actual capital stock equaled the potentialrequirement in Germanyand the UnitedKingdom and exceeded it by 7.5 percent in the United States and 3.5 percentin Austria. Clearly output was not constrained by insufficient in any of these countriesduring this period. Even were the actual capital stock to fall below the potentialrequire- ment, there would be no permanentloss of potentialproductivity, since the investment deficiency could be made good in the future and the

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E o ooNoNONON ONONONONON ONONONONONONONONN o o Robert M. Coen and Bert G. Hickman 185 growth of total factor productivity is independent of realized capital formation.48That is the basic reason for definingthe potential output path as the equilibriumgrowth path that would be consistent with continuousfull employmentof both laborand capital. Finally, what is the effect on measuredlabor productivity and invest- ment if the real wage is above the full-employmentlevel, as in figure2? Forthe given outputlevel positioningthe labordemand function, realized laborproductivity varies positively with the real wage, so that when the wage gap is positive, actualproductivity exceeds potentialproductivity. By the same token, the desired capital-laborratio, and hence actual net investment, is higherthan it would be without a wage gap.

Potential and Realized Productivity

An equation similarto equation 31 governs the behavior of realized productivityas a functionof the rate of technicalprogress, the expected wage-rentalratio, andthe rate of growthof actualman-hours, measuring the intensity of laborutilization, plus a stochastic errorterm. As may be seen fromtable 14,the growthrates of potentialand realized productivity are much the same, since they are equally affected by the underlying rate of technicalprogress; and the contributionsof the other terms, and especially of the wage-rentalratio, are highly correlated. Clearly the trendrates of actual and potentialproductivity are quite similarand not stronglyaffected by the wage-rentalgap. One expects to observe short- run fluctuations about the trend of potential productivity, however, owing to wage-rentalshocks and adjustmentlags. If the equations for realized and potential prod-uctivityare divided term-by-term,the result is an expression explainingthe ratio of realized and potentialproductivity as a multiplicativefunction of the ratio of the contributionsof the expected and potentialwage-rental rates, the ratio of actualand potential labor utilization, and the errorterm in the realized productivityequation. The termfor technicalprogress drops out because it is common to both equations. These measures are shown for each countryfrom 1966to 1984in table 16.

48. This assumes that learningby doing throughcapital formation is an unimportant componentof technicalprogress. 186 Brookings Papers on Economic Activity, 1:1987 The contributionof the wage-rentalterm depends on the size of the wage gap, since all other components of the wage-rentalratio cancel out, and on the elasticity of laborproductivity with respect to the wage- rentalratio, given by the estimatedvalue of aOin the productionfunction- about0.25 forthe UnitedKingdom and United States and0.30 for Austria and Germany.A comparisonof columns 1 and 4 for each country shows a highcorrelation between the wage and productivitygaps, as expected. However, ffictuations in labor utilization and stochastic disturbances also affect the productivitygap substantiallyin some years. Insofar as the association between the wage and productivitygaps is concerned, the principalpoint is that a positive productivitygap stemmingfrom a positive wage gap is a symptom of labor marketdisequilibrium rather than a lastingproductivity gain.

Which Full-EmploymentConcept?

Our analytical frameworkdistinguishes between the classical and Keynesian components of excess unemployment. Traditionally the definition of full employment has allowed for a necessary amount of unemploymentfor efficientfunctioning of labormarkets in the presence of internalmigration, resource reallocation, seasonal fluctuations,and job search activities. It is this concept of frictionalor structuralunem- ployment that underliesWachter's normalized unemployment measure of the naturalunemployment rate as adaptedfor this study.49 The concept of the unemploymentrate consistent with nonacceler- ating inflation (NAIRU) also posits a necessary quantity of ,and in the absence of supply shocks the naturalunem- ploymentrate is conceptuallythe same underthe two alternatives,as is clear from 'soriginal definition.50 Measurement of the NAIRU from a Phillips curve is unusually sensitive to the precise

49. Wachter,"The ChangingCyclical Responsiveness of WageInflation." 50. "The 'naturalrate of unemployment,'in other words, is the level that would be groundout by the Walrasiansystem of generalequilibrium equations, providedthere is embeddedin themthe actualstructural characteristics of the laborand markets, includingmarket imperfections, stochastic variabilityin demandsand supplies, the cost of gatheringinformation about job vacanciesand labor availabilities, the costs of mobility, and so on." Milton Friedman, "The Role of MonetaryPolicy," AmericanEconomic Review, vol. 58 (March1968), pp. 1-17. Robert M. Coen and Bert G. Hickman 187 specificationof the functional relationship, however, as may be seen from the wide rangeof empiricalestimates in the literature. NAIRU estimates by David Coe and Francesco Gagliardiare shown in table 17.51They offer two series that differ conceptually only in the specificationof the trend rate of increase of importprices and that are nonetheless strikingly dissimilar when it comes to the estimated NAIRUs. The first set uses the actual growth rate of import prices in each subintervalto estimatetrend changes in the termsof ,whereas the second uses an averagerate of growthcalculated over the estimation period (longer than the total span covered in the NAIRUs) of the underlying Phillips curves. Thus the first set responds promptly to current and recent import price shocks, whereas the second smooths them over the entire estimationperiod. Also reproducedin the table are NAIRU estimates for several countriesfrom other studies cited by Coe and Gagliardi,which againdiffer substantiallyfrom the others.52 These ambiguitiesstem partly from differingattempts to adjust for shifts in the Phillipscurve in response to supply shocks. Whenthe issue is viewed in terms of these NAIRU concepts, in other words, attention shifts from purely frictional unemploymentto unemploymentthat is needed to offset the inflationaryconsequences of supply shocks. The concept of the naturalrate has changedfrom a measureof unemployment necessary for microeconomicefficiency to one seeking to avoid accel- erating inflation from demand managementpolicies. In terms of our figure2, the supply shock that raised the actualreal wage above the full- employmentlevel is also assumed to have shifted the full-employment labor supply leftwardto a level consistent with stable inflation,creating long-termequilibrium natural unemployment as well as disequilibrium classical unemployment. The specification of the naturalunemployment rate may markedly

51. David T. Coe and Francesco Gagliardi,"Nominal Wage Determinationin Ten OECD Economies," WorkingPaper 19 (:Organization for Economic Cooperation andDevelopment, March 1985). 52. EstimatesfortheUnited States are from A. S. EnglanderandC. A. Los, "Recovery withoutAccelerating Inflation," Quarterly Review (FederalReserve Bank of New York, Summer1983), pp. 19-28;and S. Braun,"Productivity and the NAIRU(And Other Phillips CurveIssues)," WorkingPaper 34 (Boardof Governorsof the FederalReserve System, February1984). EstimatesforothercountriesarefromR. Layard,G. Basevi, 0. Blanchard, W. Buiter, and R. Dornbusch,"Europe: The Case for UnsustainableGrowth," Center for EuropeanPolicy Studies, No. 8-9 (1984). 188 Brookings Papers on Economic Activity, 1:1987

Table 17. Comparison of Estimates of the Nonaccelerating Inflation Rate of Unemployment (NAIRU), Selected Periods, 1961-83 Percent NAIRU estimates Coe-Gagliardi Average estimatesa Otherstudies" unemploy- Country Period ment rate (1) (2) (1) (2)

United States 1961-69 4.7 ...... 4.8 5.9 1967-69 3.6 4.1 5.7 ... 5.9 1970-73 5.4 6.0 5.4 6.0 5.8 1974-81 6.9 7.3 6.5 6.8 7.1 1982-83 9.7 4.2 6.1 ... 6.8 Japan 1972-75 1.5 1.2 1.2 ...... 1976-80 2.1 1.9 1.9 ...... 1981-83 2.2 2.3 2.3 ...... Germany 1967-70 1.0 0.9 0.7 1.3 1971-75 1.8 1.6 3.3 1.2 1976-80 3.6 3.1 2.4 3.5 1981-83 6.3 8.0 3.6 6.2 France 1966-70 2.1 ...... 2.2 1971-75 2.7 4.6 4.5 3.3 1976-80 5.2 3.3 4.8 5.2 1981-83 8.3 9.0 7.7 6.9 United Kingdom 1967-70 2.2 2.6 7.1 2.4 1971-75 3.0 7.2 4.2 4.0 1976-80 5.4 7.3 7.6 4.7 1981-83 10.6 5.9 9.4 9.2 1966-70 5.5 4.8 7.5 7.8 1971-75 5.8 7.2 5.4 6.6 1976-80 7.1 6.0 5.2 6.5 1981-83 9.1 6.1 5.4 7.5 1967-69 4.2 3.8 6.4 1970-73 5.9 4.1 4.7 ... 1974-79 7.2 7.2 5.8 ... 1980-83 8.5 6.9 7.4 ... Austria 1969-73 1.4 1.0 1.1 ... 1974-79 1.8 1.4 1.4 1980-83 3.0 2.4 2.4 ... 1969-73 2.5 2.2 3.0 1974-79 5.2 5.4 4.5 ... 1980-83 9.3 10.6 8.7 ... Source: Reproducedfrom Coe and Gagliardi,"Nominal Wage Determination in Ten OECDCountries." a. The NAIRU estimatesin columnI are calculatedusing the actualrate of growthof importprices; in column2 they are calculatedusing the averagerate of growthover the estimationperiod. b. For the UnitedStates the sourceis Englanderand Los, "Recoverywithout Accelerating Inflation," in the first columnand Braun,"Productivity and the NAIRU," in the second;for the othercountries the sourceis Layardand others, "Europe:The Case for UnsustainableGrowth." Robert M. Coen and Bert G. Hickman 189 affect the estimatedquantity of excess unemploymentand its breakdown into classical and Keynesiancomponents in our model. The full-employ- mentwage, and hence the wage gap, is invariantto changesin the natural rate, since the latter is not a determinantof technical progress, capital deepening, or labor utilization, and hence does not affect the path of potential productivity.An increase in the naturalrate does reduce the estimated full-employmentlabor supply, however, which means that the unchangedwage gap will account for a largerfraction of a reduced volume of excess unemployment.If a NAIRU specificationis used, and it closely tracks the actual unemploymentrate, as it usually does in empiricalestimates, there is little or no disequilibriumunemployment. Which concept should provide the basis for estimation of excess unemployment?We advocate the normalizedunemployment rate un- derlyingthe precedingtables, especiallyin view of the largeuncertainties involvingeven carefullyprepared NAIRU estimates. To quote Coe and Gagliardion the estimates reproducedabove: It must be noted that the confidenceintervals around these estimates are likely to be very large reflectingimprecise coefficient estimates and mis-specification in the wage andprice equations.For this reason, as well as the analyticfuzziness of the NAIRU concept when appliedto economies out of long-runequilibrium, the policy relevanceof the estimatedNAIRU's may not be great.53 By providinga conservativeestimate of the rise of the naturalrate from demographicand internalforces, our analysis of excess unemployment focuses on the proximatecauses of the rise of actual unemploymentin the seventies and eighties, withoutattempting a problematicbreakdown between the naturaland classical components of wage-gapunemploy- ment from supply shocks. The associated estimates of potential output also provide a superiorcapacity benchmark,since they allow only for changesin the amountof frictionalunemployment required for economic efficiency.54 A similarapproach is followed, incidentally,by Bruno and Sachs.55 It is true that they estimate a Phillipscurve that allows for the effects of changesin the productwage gap, the terms of trade, and the growthrate of full-employmentlabor productivityon consumer price inflationat a

53. Coe and Gagliardi,"Nominal Wage Determination," p. 29. 54. Our estimates of normalizedunemployment could be improved, however, by explicitlyincorporating variables directly affecting frictional unemployment. 55. Brunoand Sachs, Economics of Worldwide Stagflation, chap. 10. 190 Brookings Papers on Economic Activity, 1:1987 given unemploymentrate, and that embodies "a long-runthreshold of unemployment(like a 'naturalrate,' UNv).... This UN is definedas the level of unemploymentsuch that real is just balanced by trendproductivity growth adjusted for terms-of-tradechanges. " 56When it comes to the unemploymentconsequences of supplyshocks, however, these are estimated in a reduced form of actual unemploymenton the wage gap and on real money balances as a demandfactor. The relative importanceof the wage gap and demand factors is then discussed in terms of their contributionsto the increase of actual unemployment between 1965-69 and later subperiods, as in the updated findings of Bruno cited above.57Our approach to accounting for the proximate sources of the rise of unemploymentis clearly in the same spirit.

Policy Implications

What is the significance of our empirical measures for demand managementpolicy? A full answer is beyond the scope of this paper, since it requiresa complete model of the determinationof wages, prices, and other key macroeconomicvariables. However, some conclusions may be stated for the case where the real wage is not much altered by demandmanagement, a case broadlyconsistent with normalcost pricing and cyclical history. When excess unemploymentis largely attributableto a demandgap, considerablescope is impliedfor demandmanagement, even if the wage gap is substantial.The existence of a sizable wage gap is not primafacie evidence that classical unemployment is a dominant factor or that employmentwill not respondto demandexpansion. The gap between currentand full-employment output is a quantitative estimate of the amount of output expansion needed to eliminate that portionof excess unemploymentattributable to deficientdemand at the

56. Ibid,p. 202.The wage equationnecessary to identifythe parametersof the natural- ratespecification is not estimatedby Brunoand Sachs, however, so no empiricalmeasures of the naturalrate are suppliedin theirstudy. 57. Bruno, "AggregateSupply and DemandFactors." The same generalpoint is also valid for the importantmulticountry study of C. R. Bean, P. R. G. Layard, and S. J. Nickell, "The Rise of Unemployment:A MulticountryStudy," Economica, vol. 53 (Supplement,1986), pp. S 1-S22. They offer a similarreduced-form analysis of the role of demandand supplyfactors in the change in actual unemploymentbetween 1956-66 and 1980-83even thoughtheir model embodiesa NAIRU. Robert M. Coen and Bert G. Hickman 191 full-employmentwage level. The amountof demandstimulus needed to close the output gap will of course depend on the multiplierproperties in a given model or countryand may vary with the policy instrument. Although the utilization rate of full-employmentoutput is a direct indicatorof the output expansion requiredto attainfull employmentin a given year, the preferabletarget in a longer perspective is potential output,because capitalas well as laborwill be optimallyemployed along the naturalgrowth path. Neither concept involves a NAIRU estimateof the naturalunemploy- ment rate, for the reasons previouslydiscussed. The existence of a large demandgap implies room for substantialexpansion of employment at the given realwage anda correspondinglylarge degree of excess capacity to restrainprice pressures, but it does not provide a direct estimate of the inflationaryconsequences of an approachto full employment. Does classical unemploymentpose special problems of macroeco- nomic adjustment that differ from those associated with Keynesian unemployment?To what extent can or should classical unemployment be offset by stimulatingaggregate demand? In a completemacroeconomic model based on imperfectcompetition, firmsset prices as a markupon unit laborcosts, the markupvarying with demand conditions, so as to achieve given profit margins or rates of return.Demand expansion would thereforeimply an attemptby firmsto raise their markups in the hope of reducing real product wages and restoringor raising profit margins. If nominal wages are incompletely indexed to prices, real wages and classical unemploymentmay then be decreased along with Keynesian unemploymentby expansionary de- mandpolicy. To the extent that real wages are sticky in the face of price increases, however, firms' price-setting behavior will not easily remove a wage gap, and the risingprice level may reduce aggregatedemand through the Keynes or Pigou effects, offsetting part of the reduction in Keynesian unemploymentfor a given degree of demandstimulus. The mannerin which imperfectlycompetitive firms attempt to main- tain profit margins also has implications for the efficacy of demand managementto offset classical unemployment.While it is possible to increase labor demand at given factor prices by stimulatingaggregate demand,the demand stimulusdoes not directly address the imbalance between firms' desired rates of returnand their lower realized rates of returnwhen there is a wage gap. When unemploymentis classical and 192 Brookings Papers on Economic Activity, 1:1987 outputis at the full-employmentlevel, the wage gap shouldinduce firms to raise prices, which may or may not bring down real wages. If real wages are sticky and the gap persists, stimulationof demand, while reducing excess unemployment, may add to the upward pressure on prices by raisingcapacity utilization.The inflationaryconsequences of a given wage gap may thus be accentuatedby the demandstimulus. To offset classical unemploymentby augmentingaggregate demand, while at the same time holdingdown inflationarypressures, may there- fore requirethat demandstimulus be accompaniedby actions to sustain profits at acceptable levels-employment subsidies, investment subsi- dies, generalsubsidies to state enterprises,and so forth. Whilethe long- termeffects of such actions on economic efficiency may be undesirable, the approach may nonetheless prove superior to efforts to eliminate classical unemploymentby direct attacks on wage gaps. It is importantto bearin mindthat a full-employmentmacroeconomic equilibriumis not assured by having the real wage at the naturallevel. Output must also be at the full-employmentlevel. In a frameworkof imperfectcompetition in whichoutput is demanddetermined, an policy aimed at directly reducingthe real wage to the naturallevel may lead to a level of aggregatedemand that falls short of or exceeds full- employmentoutput, in which case demand managementmust be used in conjunction with the incomes policy to achieve full employment. Again, a full model of aggregatesupply and demandis requiredto study the efficacy of incomes policies, and the appropriatemix of incomes and demand managementpolicies may depend on the particularhistorical and institutionalcircumstances.

Conclusions

Ournew measuresidentify demand gaps as the majorsource of excess unemploymentduring 1967-74 in all the countriesin our sample except the United Kingdom. The United States, Germany, and the United Kingdom experienced chronic excess unemploymentafter 1974, but Austriaescaped their fate until 1981-84. In the United States, the wage gap has increased in importanceespecially since 1974, but aggregate demandhas remainedthe dominantdeterminant except in isolatedyears. Thewage gapin Germanywaxed andwaned during 1973-84, but classical unemploymentwas never the dominantfactor. Excess unemployment Robert M. Coen and Bert G. Hickman 193 was minimizedin Austria during the 1970s by offsetting demand and wage gaps. Althoughnot the dominantcomponent in most years since 1974,classical unemploymenthas usuallybeen substantialin the United Kingdom.The sharprun-up of unemploymentin all the countriesduring the 1980s was induced primarilyby deficient demand, althoughit was substantiallyaugmented by largewage gaps in the United Kingdomand the United States. Hiddenunemployment is quantitativelyimportant in all the countries, so thatelimination of the employmentshortfall would reduceunemploy- ment by a considerablysmaller amount in most years. This is especially trueof Austriaand the United States, where the employmentelasticities of laborforce participationare largerthan they are in Germanyand the United Kingdom. Inverse responses of average hours substantiallymitigated the em- ployment improvements from the simulated wage reductions in all countriesexcept the United States, where the inducedrise in hours was small. The implication is that empirical studies that abstract from endogenous changes in hours may seriously overestimate the wage elasticity of employment. The findingof large and growing demand gaps in the 1980s implies that expansionary monetary and fiscal policies would act to reduce unemploymentin these countries.As mentioned,our partial-equilibrium measures provide quantitativeestimates of the output expansion that would eliminateKeynesian unemployment were the real wage invariant to demand expansion. Since the real wage is an endogenous variable, however, the classical component of unemploymentcould increase or decrease in the process of demand expansion, and a complete policy prescriptionis beyond the scope of this paper. Irrespectiveof equilibriumNAIRU calculations, importprice pres- suresin the Europeancountries have been eased substantiallyby reduced oil prices and a weak dollar, and our low potentialutilization estimates for Germanyand the United Kingdom indicate a considerablemargin for expansionwithout undue pressure on markups.Finally, if there is an elementof in the naturalrate, as in the insider-outsidertheory of Blanchardand Summers, a demand expansion that reduced actual unemploymentwould also reduce the NAIRU.58

58. OlivierJ. Blanchardand LawrenceH. Summers,"Hysteresis and the European UnemploymentProblem," Working Paper 1950 (National Bureau of EconomicResearch, June1986). Comments and Discussion

Stephen M. Goldfeld: The interestingpaper by Robert Coen and Bert Hickmanis motivatedby one of the importantquestions of this or any other day-the sources of unemploymentboth here and abroad. The paper explores the intuitively appealing notion that both aggregate demandand realwages have a role in the explanation.More specifically, it provides a methodologyfor sortingout the relative effects of each of these variables and carries out this "unemploymentaccounting" for four countries. In discussing the paper, I first briefly examine some features of the underlyingmodel. I then turn to the question of the potential sensitivity of the unemployment accounting to alternative assumptions. Finally, I consider the somewhat harder issue of what questions the numbersand methodologyare providinganswers to. Coen andHickman characterize their model as supplyinga framework consistent with the assumptionof imperfectcompetition in the presence of .While this is generallya fair characterizationthere are a few elements of inconsistency that are worth noting. One feature of the model is that capital and labor inputs are viewed as chosen so as to minimizethe cost of producingthe expected level of output.Presumably more relevant is the choice of inputs so as to minimizeexpected cost, but this is a ratherminor inelegance. A bit moreinelegant is the fact that adjustment costs are posited to lead to separate partial adjustment models for capital and labor, although this too is a feature of other models. The treatment of adjustmentraises some other issues. Given the partialadjustment of factor inputs in the Coen-Hickmanmodel, in the short run firms end up off their long-run production function. Firms compensatefor this by endogenouslyadjusting the utilizationof capital

194 Robert M. Coen and Bert G. Hickman 195 and labor. Whether this makes sense in all circumstances obviously depends on one's views of the underlyingtechnology, that is, of the scope for ex post substitutabilitybetween capitaland labor. The endogeneity of capacity utilizationalso raises a question about the natureof the underlyingprice equation.In the Coen-Hickmanmodel prices are determinedby a markupover normalunit laborcosts but also depend on import prices and capacity utilization. The presence of the lattervariable suggests that price-settingbehavior should therefore take account of the adjustmentcosts drivingthe partialadjustment of inputs. This interconnectionbetween pricingand factor adjustmentsseems to be missingfrom the model. On the other hand, since the price equation is ignored in the unemploymentaccounting, except for the possible reverse effect of the pricing on the adjustmentof capital, this point is somewhatmoot. On the whole, while one may quibble with various features of the Coen-Hickmanmodel, these are hardlythe majorissues in the context of the paper. A more serious set of questions concerns the details of the unemploy- ment accountingand the potentialsensitivity of the numericalresults to alternativeassumptions, either as to the specificationof the estimated equations or as to the general structureof the model. To begin with, even takingthe specificationof the model as given, the stochastic nature of the estimatedequations means that the unemploymentaccounting is subject to uncertainty.Unfortunately no measures of this uncertainty are provided, so we remainunsure as to the precision of the split into wage and demandgaps. Once we recognizethe possibilityof alternative specifications,the robustnessissue is even more critical. That this is of some potential relevance is suggested by the observationthat some of the key elasticitiesin the presentmodel appearnoticeably different from those of other researchers.Another example is providedby the natural rateof unemployment.In the presentpaper, the naturalrate is determined by purely demographicconsiderations and is driven by the prime-age maleunemployment rate. Needless to say, there are alternativeways to generatethis benchmarkrate and, as Coen and Hickmanacknowledge, the particularnumbers used will have a direct effect on the accounting exercise. A ratherdifferent sort of sensitivity issue is raised by the treatment of capitalgoods prices in the model. To use the model one needs the real 196 Brookings Papers on Economic Activity, 1:1987 wage expressed in terms of both consumer and capital goods prices, and, as a simplification,Coen and Hickmanassume that one can ignore the differentialtrend in consumer and capital goods prices along the potentialpath. By their own numbers, admittedlyfor the actual rather than potentialpath, this assumptionappears a bit problematic. A closely relatedissue concerns the adjustmentsmade in response to the first oil shock. The unanticipated increase in import prices is characterizedas raisingthe prices of investmentgoods relativeto money wages and is dealt with by imposing on the full-employmentpath an exogenous downshiftin the real wage of 7 percent. As one justification for this, Coen and Hickman state that the oil shock induced a lasting increase of about 5 percent in the ratio of the price of capital goods to finaloutput. It is clearthat the initialeffect was of this orderof magnitude, at least if one uses implicit deflatorsrather than fixed-weightindexes. Indeed, using the latest GNP data, the relevantratio goes from 0.929 in 1973to 0.976 in 1975. However, by 1984, the ratio has fallen to 0.915, below its level in 1973.While these numbersare not definitiveas to what would happenalong a potentialpath, the assumed permanentnature of the changes is open to some doubt. Indeed, the authors allow for a second shiftin the 1980s,arising this time fromthe dollar'sappreciation. A perhaps more satisfactory way to deal with this issue would be to model explicitly the behavior of investment good and final good prices in response to importprice changes. A somewhatdifferent issue concerningthe unemploymentaccounting is the treatmentof the so-called carryoverunemployment. Because of the existence of adjustmentlags, even if outputand the real wage are at their full-employment values, the economy will not be in long-run equilibriumunless last period's man-hourswere also at the full-employ- ment level. The partof unemploymentattributable to this laggedadjust- ment is carryoverunemployment. Although in some earlierwork Hick- man reportedcarryover unemployment separately, in the present paper it is lumped in with unemploymentdue to inadequatedemand. While this is to some extent semantics, I would have preferredthe earlier treatmentsince it strikesme as a bit unreasonableto contemplatedriving output above potential output to compensate for past shocks and for policy errors. As this suggests, one's preferredtreatment of carryover unemploymentis relatedto the moregeneral issue of how one interprets the results of an unemploymentaccounting exercise. Robert M. Coen and Bert G. Hickman 197 Broadly put, the key question is what we learn by an allocation of unemploymentinto real wage and aggregatedemand components. Coen and Hickman suggest that such an allocation indicates the "proximate causes" of unemployment. They also indicate that their allocation utilizes demandfunctions conditionalon real wages and output. Some care is needed in interpretingthis statementbecause however Coen and Hickmanchoose to regardoutput and the real wage, the datathey utilize emergefrom a real where output, the real wage, and the variables they analyze explicitly are all jointly endogenous. Potential technicalitiesaside, it is somewhatunclear as to the sense in which the Coen-Hickmancalculations yield proximatecauses. Other attempts at unemploymentaccounting have considered a wider range of potential explanations such as , union power, skill or regional mismatches, and public unemployment,to name a few. How these sorts of considerationsshould be integratedwith wage gaps and demand gaps is not really clear, in part because the unemployment accounting exercise does not seem to give answers to any well-posed question. What lies behind ' interest in unemploymentaccounting is the possibility of extractinga message for policymakers. One temp- tation is to leap from Coen and Hickman'sfinding that unemploymentis due to a demandgap to the conclusion that aggregatedemand manage- ment is called for. The companiontemptation is to conclude that a real wage gap may call for other sorts of policies. Unfortunately, in the absence of an explicit model as to how policy operates, neitherof these conclusions may be warranted. Output may be below potential, and there may be limited scope for demand . Alternatively, there may be a wage gap that is fully curable by aggregate .Robert Solow, for example, has provided an illustrative model in which the real wage is too high at the same time that output is below potential but where expansionarymonetary policy can cure all gaps.' On balance,then, while tantalizinglyinteresting, the sorts of numbers presented by Coen and Hickman need to be supplementedwith more structureto make them fully interpretableand more useful for policy purposes. 1. Robert M. Solow, "Unemployment:Getting the Questions Right," Economica, vol. 53 (Supplement,1986), pp. S23-S34. 198 Brookings Papers on Economic Activity, 1:1987 : In the best Brookings Panel tradition, this paper is motivated by crucial current issues of macroeconomic diagnosis and prescriptionand brings sophisticated analytical and empiricaltools to bear on them. Is the high unemploymentof the 1980s "classical" or "Keynesian"? Is it attributableto stubbornlyexcessive real wages? Or to shortfallsin effective demand?Would expansionaryfiscal and mon- etary policies just cause inflation?Or would they add to real output and employment?These timely questions are especially relevantto Europe, but they apply also to Japan,where the unemploymentis disguised, and to the United States, where the economy has settled into rates of unemploymentand excess capacityhigher than those in previouscyclical recoveries. I applaudCoen and Hickman for their audacious and ingenious attempt to quantifyconcepts so importantin macroeconomictheory and policy, especially because they confirmmy own priorsthat most unemployment beyond the rates of the late 1970sis Keynesian. Those bouquets are a sincere prelude to the doubts I am about to express. Do the authorsreally answer the questions that concern policymak- ers? The -pessimists or Euro-hypochondriacsforswear demand stimulus because they believe it will be inflationary.They think that require higher profit margins to expand production, that workers won't permit them, that unions will demand still higher real wage rates if enhances their bargainingpower, that the NAIRU has shifted many points in the wrong direction. Sometimes the Europeanposition appearsto be that demandexpansion is inflation-safe only if it is naturally generated by export markets or spontaneous domestic demand,never if it is contrivedby government. The authors'findings will not reassureEuro-pessimists who thinklike that. Coen and Hickmantell them they have a lot of Keynesian unem- ployment-the more so because some is "hidden"-but they cannot assure them that Keynesian remedies will be noninflationary.The authors' full employment, which corresponds to their "natural-rate" unemployment,is not the NAIRU. I endorsethe distinctionin principle, without understandingwhy the 3 percent unemploymentrate of males aged forty-fiveto fifty-fourin 1956is the benchmarkfor full employment in the United States. The authors do not say what would happen to moneywages, realwages, andprices if demandstimulus were undertaken to reachfull employment.Their findings should be somewhatreassuring, Robert M. Coen and Bert G. Hickman 199 because they show there is plenty of room in the economies they study to enable productionto respond to demand. But they don't dispel the fears of sectoral bottlenecks, structuralrigidities, and distributional conflicts that Euro-pessimistscite as obstacles to noninflationarymac- roeconomic expansion. Whatis missingfrom the authors'model is a relationshipbetween the Bruno-Sachswage gap and the Okun output gap. Coen and Hickman decompose shortfallsin employmentand productioninto classical and Keynesian components. Their additive decomposition is simple and neat, and their idea that the two types of unemploymentcan coexist is appealing. But the implication that the demand constraint could be removedwithout affectingthe real wage is suspect. I sketched above the likely suspicionsof a Euro-pessimist.A General TheoryKeynesian might have quite the opposite suspicion. He could say that the real wage is high because demand is short. Thanks to competitionamong employers, even when there is an overall effective demandconstraint, workers lucky enoughto havejobs are paidfar more thantheir reservation wages. Expansionitself will dissipatethese rents. The unemploymentmay look classical, but the wage gap is a miragethat will vanish en route to prosperity. Which scenario, pessimistic or optimistic, applies to the countries and periods under study is an empiricalquestion. Theory tells us little about relations amongthese variablesin disequilibrium.Economic and political institutionsmatter, and the findingsare likely to differ among national economies. a few years ago was that nominalwage inertiacharacterized the United States and United King- dom, while continental European economies suffered from real wage inertia. Robert Gordon questions that in a recent paper, and I will let him speak for himself.' I allow myself a digression from the authors' text. The failure of inflationto fall precipitously in economies where unemploymenthas been so high so long suggests to some observers that the NAIRU has risen many points. If you are sure of the slope of the short-runPhillips curve, you will explain the slow attritionof inflationin the 1980s by a large adverse shift in the curve. The implicationis that demandexpan- sion, startingfrom unemploymentrates around 10 percent, will accel-

1. RobertJ. Gordon, "Productivity,Wages, and Prices Inside and Outsideof Manu- facturingin the U.S., Japan, and Europe," EuropeanEconomic Review, vol. 31 (April 1987), pp. 685-733. 200 Brookings Papers on Economic Activity, 1:1987 erate prices. I find the conclusion unconvincing,given the absence of recent experiencewith demandexpansion. Maybethe short-runPhillips curveis nearlyflat in the previouslyvirgin territory of 1980sobservations; maybe the paths of wages and prices are pretty much detachedfrom the size of the Okungap. The potentialoutput path is crucialto the calculationsof the real wage and outputgaps and of the decompositionof unemploymentinto the two types. The path, as I understandit, is essentially a track familiar in neoclassical growththeory with one productand two factors, labor and capital. Of the family of tracks consistent with the technology, the authors' path is the one that has an after-tax return on capital of 6 percent. The related "rental cost of capital" is, however, not strictly constant but varies with the tax treatmentof depreciationand invest- ment. It is gratuitouslyassumed that saving would always match the capitalaccumulation implied by the path. The uniquenessof the potentialoutput path and the neglect of the IS equationseem to me to limit the usefulness of the paperfor policy. How demandstimuli might eliminate Keynesian unemployment, and how the mix of monetaryand fiscal policy might affect potentialoutput, cannot be analyzed. I should think that how the capital investment impliedby the authors' model is financed would affect real interest rates and the growthpath itself. The authors' potential output does not depend upon the history of actual output. No matter how much and how long actual output falls short, its shadow marches on in splendid detachment. The authors blithely observe that deficiencies of capital and labor inputscan always be repairedin the future. Here again, the absence of a savingfunction is crippling.It may or may not be so that savers, as well as , will eventuallyaccumulate wealth and capitalto the same multiplesof poten- tialoutput whether interrupted by anddepressions or not. But surelyafter a decadeof stagnationit wouldtake a longtime to builda capi- tal stock of normalsize. Presumablythere would also be lastingdamage to humancapital. Now that the has rediscovered the fancy word hysteresis, it is respectableto mentioneffects of this kind. The model assumes constant-returns-to-scaleCobb-Douglas tech- nology, with capital exponent a. and Hicks-neutralprogress at rate P, thus Harrod-neutral labor augmentation at rate ,/(1 - cx).Neither , nor the rate of growthof the naturallabor force is constant. Nonetheless the Robert M. Coen and Bert G. Hickman 201 exogenous inputthat drives the growthof potentialoutput is augmented labor. The equilibriumcapital stock along the path correspondsto the ratio k* (my notation) of capital to augmented labor that yields the requiredrental. This ratio will be roughlyconstant. The same k* determinesthe near-constantreal wage w* (my notation) of augmentedlabor, fromwhich can be derivedthe real wage for natural labor, growing at rate 3/(l - a.). The w* path could be regarded as the referencepath for calculatingthe wage gap and classical unemployment. Suppose the actual productivity-adjustedwage w is higher than w*. Assume with the authorsthat the supply of is perfectly elastic so that the rental cost of capital q (the authors' q, not mine) stays put. We know that in Cobb-Douglastechnology k = [o/(1 - o)](wlq), and of course k* = [o/(1 - o)](w*Iq). A higher wage-rental ratio requires a proportionatelyhigher k and implies less L or more K for any given output. The cost-minimizingresponse of a typical firmto a 1 percent increase in the wage-rentalratio is, as just argued,to raise k over k* by 1 percent. Producingthe same outputas before, the firmwould use (1 - a.)percent more capitaland a.percent less labor. The latteris the authors'estimate of the classical unemploymentdue to the rise in the wage relative to the rentalcost of capital. But it is not the profit-maximizingsolution. At that output,the firmwould be makinglosses unless the productprice rose by (1 - a.)percent relative to both the new wage w and the rentalq. In terms of product, the wage gap would be only cxpercent, and the rental cost would have fallen by (1 - cx)percent. It is hard to conceive a model of savingand investmentthat would, with income unchangedand capital's returnlower, providethe additionalcapital in the short or long run. The response of employmentto a realwage increaseinvolves not only substitutionof capitalrelative to labor (higherk) but also adjustmentof output. Economists who have emphasized the recent importance of classical unemploymenthave arguedthat excessive real wages limit the supplyof output even when it is below potential. Were there a positive wage gap at or below full-employmentequilibrium, firms would find it unprofitableto produce that much output and offer that much employ- ment. In contrast, profitabilityis not an effective constraint in the authors'model; outputis always constrainedby demand. An easy way to see this difference in the role of profitabilityis to consider the special case where the supply of capital K is inelastic. As 202 Brookings Papers on Economic Activity, 1:1987 conceived by the authors, classical unemploymentwould be zero. An increase in the real wage would simplydrive up the rentalcost of capital untilfirms desired to producethe fixed, demand-constrainedoutput with the same inputof labor,that is, untilthe incentiveto substituteone factor for the other was removed. Of course, if firmswere just breakingeven beforethe wage increase, they wouldnow be runninglosses. The authors assumethat somehowfirms will findit profitableat the marginto produce up to the demandconstraint. Traditionalclassical unemployment,on the otherhand, would be very large. Profitability,not demand,would become the effective constraint. Full profit-maximizingadjustment to a 1 percent real wage increase would requirea decrease of 1/a percent in employmentand of (1 - cx)/cx percent in output-4 percent and 3 percent, respectively, with the authors'estimate of cx,0.25. It is in the natureof classicalunemployment, in contrast to Keynesian unemployment, that it is due to real wage rigidity, so that a rise in the nominal price of output offers no escape from this scenario. In general, the relationshipbetween output prices and capital goods prices mustbe madeexplicit. In a one-productmodel, capitalinvestment is simply one use of currentoutput, which otherwise can be consumed. Movementsin the productprice do not alter the rentalcost of capital. If operationof the existing capital stock is unprofitable,accumulation of capital will be unprofitable.As the stock is run down by depreciation, furtherreductions in output and employmentwill occur. A two-sector model, distinguishingcapital goods productionfrom consumer goods production, would be a cleaner way to proceed. The authors' use of capital goods prices as numeraireleads to confusion in definingwage gaps. Classical unemploymenthas traditionallymeant not just rigidlyhigh real wages but also concurrent of capital and, in a closed economy, of accumulatedsavings. Coen and Hickmansimply wave that constraintaway. If the capitalstock can be assumedto adjustas needed to preserve output in the face of a wage gap, why not go further and assume it can adjust enough to preserve employment? A 1 percent increase in K, with appropriatereduction in capital cost to preserve profitability,would validatethe 1 percent increase in the real wage with no loss of employmentand an cxpercent gain in potentialoutput. Robert M. Coen and Bert G. Hickman 203 Suppose the economy shows by the authors'calculations both kinds of unemployment.The authors say that demand stimulus can remedy the Keynesianunemployment while the wage gap remains.Their decom- position of unemploymentassumes that duringthe demandand output expansion, capital accumulationwill be greater than in the absence of the wage gap. Investment will include "deepening," substitution of capitalfor labor, as well as "widening." This scenario is not subject to my objection above if the expansion itself can generate the necessary extra saving. That depends on the nature of the demand stimulus; a Reagan-Volckerfiscal-monetary mix could hardlybe expected to do the job. On the investment side, one might doubt that in times of excess capacityand high real wages businesses will feel preparedboth to expand capacity and to install labor-savingequipment. A specific problem the authors faced was to modify their potential outputtrack to allow for the impactof the energy shock of 1973-74. I am mystified by their resolution of this problem. One obvious step is to reduce the estimated rate of progress c in the productionfunction to allow for the lower growthof productivityobserved, whateverits cause, after 1974. An additionalpossibility would be a one-shot reduction in the scale constantA in the productionfunction. However, it is not clear to me why an increasein the relativeprice of oil and energy shouldlower the capacity of domestic industries,including energy producers,to add value at constantprices. I don't see the relevance of the adverse shift in external terms of trade. I don't see why a jump in energy prices is modeled as a jump in capital goods prices necessitating a once-for-all decline in potential output in order to maintainthe requiredreturn on capital. In effect, what the authorsappear to have introducedis a direct one- shot 7 percent downwardadjustment of the equilibriumproduct wage. The result is a largerwage gap and classical unemployment,despite the fact that in the United States actual real wages, whetherin terms of the authors' numeraire,capital goods, or of consumer goods, were falling significantly.It is neither contradictoryto the authors' own concepts nor otherwise unreasonableto regardmuch of the unemploymentin the United States in 1976-82 as Keynesian ratherthan classical unemploy- ment, toleratedand generated by the monetaryauthorities to oppose the inflationbrought by supply shocks and other events. 204 Brookings Papers on Economic Activity, 1:1987 The authors say that their model is based on imperfect, not pure, competition. Operationally,this is theirjustification for derivingfactor demandsfrom cost minimizationrather than ,and for assumingfirms are always demand-constrained. I conjecturethat Coen and Hickmanhave in mind somethinglike the followingas the way imperfectcompetition enters their model of potential output:a typical firm,a price-setterin productmarkets but a price-taker in factor markets,does not equate the marginalproduct (MP) of laborto the real wage or the MP of capitalto its rentalcost. The firmequates the marginalrevenue product of each factor to its price. The MRP in each case is MPI(1+ ,u),where pLis the markupin proportionto marginalcost. For the long-run calculations relevant to the growth track, constant imply that marginalcost equals and is constant. The markup pLcan also be identified as the "degree of " and is equal to - 1/(1+ q), where -q(< - 1) is the elasticity of demandfor the firm's product with respect to its relative price. For the short run, the authorsassume a markupover laborcost alone. Since wage cost is normallya fraction(1 - a.)of total cost per worker,I suppose this markup is (. + I)/(q+ a). These markups,related to the degree of monopoly, bringmonopoly- rent incomes. They would have to be taken into account in a complete model, particularlyin relation to consumption, saving, and taxation. However, a serious imperfect-competitionmodel would not assume constantreturns to scale for an individualfirm. It would assume instead that a firm has increasing returns because of fixed costs required to establish and maintainproduct differentiation. Then the markupscould be partiallyor wholly swallowed by those costs, as in Chamberlinian monopolisticcompetition. In distinguishingtheir model from other disequilibriummacroeco- nomic models, the authorsassert, "Keynesian and classical unemploy- mentmay coexist ratherthan occurring in separateregimes. " Evidently, a separateclassical regime is ruled out by the assumptionof imperfect competition, since firms are always constrainedby effective demand, withprice exceeding . Even in full-employmentequilibrium such a firmwould want to satisfy at prevailingprices additionaldemand due to an outwardshift of its demandcurve. But if all firms, all typical, tried to do so, the aggregate supply constraint would bind. It, not demand, is the effective constraint. The situation is not so differentin Robert M. Coen and Bert G. Hickman 205 the purelycompetitive model. Theretoo, given constantreturns to scale within firms or by multiplicationof firms, output will respond to new demandat prevailingprices if andonly if economywideresource supplies permit. Likewise in both cases individualfirms may or may not be in local marginal-revenue-equals-marginal-costsituations. Macroeconomicdisequilibrium models, whatever their microfoun- dations, should not suggest that outputsand sales of individualfirms are rationed. Both demand and supply constraints should be modeled as economywide limits that lead individualfirms to decide not to produce or sell more. My final comment refers to the authors' model of adjustmentsof employment and capital stock to their desired values. They talk of adjustmentcosts but do not explicitlyintroduce them. They use separate annualrates of stock adjustmentfor the two inputs. The desired stocks towardwhich the firmmoves are derived from currentvalues of output (demand)and factor prices, even though the firm will not reach those targetsfor many years. The labor adjustmentis the faster, but it surely does not minimizecosts along the way to employ labor as if the capital adjustmentwere complete when in fact it is not. An attractivefeature of the model is the explicit distinction between numbers employed and hours of work. Why can't short-runadjustment of labor input be made in hours of work? Surely the properstrategy is to find a desired path of employment,hours, andinvestment, given the expected pathof demand, such that the present value of costs, production plus adjustment, is minimized.

GeneralDiscussion

Robert Gordon questioned the very low naturalrates of unemploy- mentcalculated for the three Europeancountries by Coen andHickman. He arguedfor definingthe naturalrate of unemploymentas the NAIRU- the rate consistent with steady inflation-rather than in terms of labor marketefficiency as the authors attempt to do. His own estimates for Europe as a whole based on wage and price equations show the 1984 naturalrate to be in the vicinity of 6.0 to 6.5 percent, ratherthan the 1.0 to 2.0 percentCoen and Hickmanassume for Germany,Austria, and the UnitedKingdom. 206 Brookings Papers on Economic Activity, 1:1987 Katharine Abraham suggested that the authors' estimates of the naturalrate should consider factors other than demographicsthat may have affected the volume of frictionalunemployment. She noted that in the United States and the United Kingdom, the inverse relationship between prime-agemale unemploymentand vacancies has shifted out- wards over time, suggestingthat, at least in these two countries, other sources of frictionalunemployment have grown in importance. EdmundPhelps explained why, even if one agreed with the authors that Keynesian shocks generallyexplain the lion's shareof employment fluctuations,it does not follow from their analysis that the severe 1980s slump in Europe is predominantlyKeynesian in origin. The derived demandfor labor curve to which Coen and Hickmanrefer-their LD- may have shifted down in this decade due to the increased markup desired by customer-marketfirms in response to the sharp rise in real interest rates, as arguedin a recent paper by Phelps and J.-P. Fitoussi, ratherthan because of Keynesian shocks.' Gordon remarked that the absence of dynamic wage and price equationslimits the usefulness of Coen and Hickman'sapproach. Even thoughcurrent real wages may not be far out of line, they may have been reducedin response to economic slack. Policymakersmay fear that they would rise sharplyif aggregatedemand were now stimulated. MartinBaily commentedthat the authors'decomposition of "excess" unemploymentinto classical and Keynesian components is extremely sensitive to assumptionsabout what is fixed and whatis allowed to vary. As Coen and Hickmannote in theirpaper, in a simplemodel with Cobb- Douglasproduction and no adjustmentlags, the output-constantelastic- ity of demandfor laborequals the inverse of capital's shareif the capital stock is assumedfixed, but equals capital's shareif the rate of returnon capital is held constant while the capital stock is allowed to vary. If capital's share is assumed to be about 0.25, the demand for labor is sixteen times more elastic under the first assumption than under the second.

1. J.-P. Fitoussi and E. S. Phelps, "Causes of the 1980sSlump in Europe," BPEA, 2:1986, pp. 487-513.