Real wages, aggregate demand, and unemployment

European Economic Review 31 (1987) 1531-1560. North-Holland

REAL WAGES, AGGREGATE DEMAND, AND UNEMPLOYMENT Bert G. HICKMAN* Stanford Unit'ersit}" Stanford, CA 94305, USA

Received February 1986, final version received July 1986 A new methodology for differentiating the effects of aggregate demand and real wage rigidity on unemployment is presented, It departs from the standard fixprice model by specifying that (1) product markets are imperfectly competitive and (2) demand functions for labor and capital are conditional on output as well as on the real wage. Keynesian and classical unemployment may coexist instead of occupying separate regimes as in the rationing model with competitive firms. The method is used to estimate the volumes of natural, excess, hidden, demand gap, and wage gap unemployment in the United States during 1959-1982.

1. Introduction

One of the key issues in macroeconomics concerns the role of high real wages as a cause of unemployment. A number of authors have argued that excessive levels of real wages are primarily responsible for unemployment in many OECD countries since the early 1970s [see the introduction to Bruno and Sachs (1985) for a summary and references]. An extensive theoretical literature has also developed to explain the difference between classical and Keynesian unemployment regimes, as in the general disequilibrium or nonmarket-clearing models of Barro and Grossman (1971) and Malinvaud (1977). A new method for differentiating the effects of aggregate demand and real wage rigidity on unemployment is proposed in this paper. It is related to the 'wage gap' analysis stressed by Bruno and Sachs but, unlike their concept, it builds on the hypothesis of imperfect competition in the product markets and on cost-minimization rather than profit-maximization as the basis for labor demand. Since labor demand is conditional on output as well as on the real wage, unemployment may exceed (or fall short of) the natural level even if the real wage is at the level which would clear the labor market at the *This paper is part of a research project on Unemployment, Real Wages, and Economic Growth which is being undertaken jointly with Robert M. Coen. The support of the Oesterreichische Nationalbank through the Jubilaeumsfons is gratefully acknowledged. I am indebted to Erich Streissler, Stefan Schleicher, Robert M. Coen, Stephen King, George Evans, Jean Waelbroeck, and seminar participants at the University of Vienna, Project LINK, and Stanford University for their comments and suggestions. 0014-2921/87/53.50

©

1987, Elsevier Science Publishers B.V. (North-Holland)

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B.G. Hickman, Rea/wages, aggregate demand, and unemployment

potential level of output. Classical and Keynesian unemployment may coexist and are not separate regimes, as they are in models with price-taking firms and rationed buyers or sellers in the market for goods. In addition to providing an analytical framework for distinguishing the classical and Keynesian components of observed unemployment, the paper presents empirical estimates from the Hickman-Coen Annual Growth Model (1976) of the relative importance of demand shortfalls and wage gaps in the unemployment history of the United States during 1959-1982. It is beyond the scope of the present paper, however, to account for the persistence of a positive wage gap through most of the period or to assess the factors responsible for the occurrence of the observed fluctuations in aggregate demand.' 2. Fixprice models of classical and Keynesian unemployment The general disequilibrium or non-market-clearing model distinguishes Keynesian and classical unemployment states as separate regimes under fixed wage and price levels by incorporating quantity constraints into the optimization problems of firms and households.' The representative firm is a price-taker in its markets for inputs and output. It maximizes profits, pY-wL-qK,

(1)

subject to a well-behaved production function, Y=F(L,K),

(2)

and a product demand constraint,

(3) where Y, K, and L are output, capital stock, and manhours, respectively, p is output price, w the nominal wage, q the nominal rental price of capital, and Y the perceived level of demand. The firm is rationed in the output market if (3) is binding (Keynesian unemployment), but otherwise it is free to choose the unconstrained optimum for L, K, and Y (classical unemployment). For 1 Research is underway to construct similar, though smaller, models of several OECD countries to facilitate comparative analysis of the relative importance of real wage gaps and Keynesian demand deficiencies in their recent unemployment history. It is hoped that these new measures for the United States and other countries will prove useful in future investigations of "these important questions concerning the performance and prospects of the market economies. 2Basic references include Patinkin (1956), Clower (1965), Barro and Grossman (1971), Malinvaud (1977) and Benassy (1975, 1982).

B.G. Hickman. Real .....ages. aggregate demand. and unemployment

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fixed K in the short run, the optimal solution for L is the min-equation (4)

and the corresponding solution for Y is Y*=min [F(F-I(Y,K), K), F(Fi I (w/p, K), K)].

(5)

The unconstrained or notional functions for labor demand and product supply are (6)

given by the first-order marginal productivity condition, and (7)

The classical labor supply function is L'=L'(w/p),

(8)

where the real wage equates the marginal disutility of effort and the marginal utility of consumption. With flexible wages and prices, a Walrasian solution of (6) and (8) would yield full employment at the equilibrium real wage. With fixed wages and prices, however, if notional supply exceeds effective demand at the given price, the sales of firms are rationed in the product market. Labor demand is then output-constrained and is smaller than labor supply at the existing real wage, resulting in Keynesian unemployment: (9)

Thus, Keynesian unemployment is the spillover effect of disequilibrium in the product market. Classical unemployment may occur if the fixed price is below the Walrasian equilibrium level. Effective demand then exceeds notional 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 unconstrained and operating on their notional labor demand and output supply schedules, but since the real wage exceeds the Walrasian level, labor demand falls short of full-employment labor supply. In both unemployment states households are constrained in the labor market and hence effective demand falls short of the notional demand which

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B.G. Hickman, Real wages, aggregate demand, and unemployment

would result from unconstrained utility maximization. Indeed, as Clower (1965) showed, it is because of the spill-over from the labor market constraint that income is an argument in the consumption function. Aggregate demand is a decreasing function of price because real money balances are included in the utility function and the nominal money supply is exogenous [Barro and Grossman (1971), Benassy (1982, ch. ttl], The approach of this paper modifies the standard fixprice model in two principal respects. First, imperfect competition is assumed, so that firms are price-setters facing uncertain demands. Second, firms choose capital and labor inputs so as to minimize the cost of producing the quantity they expect to sell at the price they have set. The assumption of imperfect competition is adopted on both theoretical and empirical grounds. Perfect competition among atomistic price-taking firms is basically incompatible with the fixprice assumption except for very short adjustment periods after unexpected shocks. As an empirical matter, moreover, auction markets are largely limited to agricultural products and primary metals. There is also solid econometric evidence of the ubiquitous existence of cost-based price-setting, with only a limited scope for markup variations in response to shifts in product demand [Eckstein (1972), Cagan (1974), Nordhaus (1974)]. Market imperfections provide a theoretical rationale for the fixprice assumption. One major theoretical construct incorporates the perceived asymmetry of competitors' responses to a firm's potential price increase or decrease in oligopolistic industries as the source of price rigidity, as in Sweezy's (1939) theory of the kinked demand curve. Similarly, in Negishi's (1979) conjectural equilibrium model of atomistic firms, a kink in the perceived demand schedule exists because of the asymmetric reactions of consumers to price changes: Lower prices asked by a supplier may not be fully advertised to customers currently buying from other suppliers who are maintaining their current price, while a higher price charged by the same supplier necessarily induces present customers to leave in search of lower price suppliers (p. 87).3 Imperfect information and search processes are also central to Okun's (1981) customer shopping model, with added stress on the desire of sellers to maintain strong long-term customer attachment to their products by forgoing price adjustments to temporary demand fluctuations. In all these formulations, shifts in demand initially lead to a change in the quantity sold at the current price and may leave the price permanently unaffected, so that fixprice or rigid price is explained rather than assumed. lHahn's (1977,1978) model of conjectural equilibrium is similar to Negishi's, but does not assume a kink in the perceived demand curve.

B.G. Hickman, Real wages, aggregate demand, and unemployment

1535

Under imperfect competition, the firm expects to sell output Y when it sets price a P. Expected revenue is predetermined and the firm minimizes production costs,

C(Y)=IVL+qK,

(10)

to determine factor demands. If K is assumed to be fixed as in the standard fixprice model, Ld will again be given by (9). If substitution of capital and labor is taken into account, however, the labor demand function becomes conditional on the wage-rental ratio as well as on output: (11)

The replacement of (4) by the conditional labor demand function (11) is the key to the new method of allocating unemployment in this paper. Since the rental price of capital includes the price of (capital) goods along with the discount and depreciation rates, labor demand depends on the real wage as well as on output, in contrast to the discrete classical and Keynesian dichotomy in (4). Labor demand can therefore fall short of full employment either because effective demand is too low or because the real wage is too high, or both. Keynesian and classical unemployment may coexist rather than occurring in separate regimes as in the standard fixprice disequilibrium model. Classical unemployment is ruled out as a discrete state with firms on their notional supply schedules and households rationed off their demand schedules, but classical unemployment may still occur in the absence of Keynesian unemployment provided that a positive wage gap (the real wage is above the full-employment level) exists without an accompanying demand shortfall. 3. An empirical-growth model The empirical results presented below are derived from stand-alone simulations of the labor market sector of the Hickrnan-Coen (HC) Model, treating expected output and the expected real wage as predetermined variables in the conditional labor demand function. The HC Model is a complete general equilibrium system combining Keynesian and neoclassical elements and allowing for departures from the full-employment growth path owing to deviations between effective demand and supply. A brief description of its general structure will suffice for present purposes, since this paper is not concerned with the endogenous determination of effective demand or the absolute levels of wages and prices, and the estimates of classical and Keynesian unemployment depend only on the labor equations. The labor market specification and the determination of potential labor force and 40riginal footnote deleted.

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B.G. Hickman, Real wages, aggregate demand, and unemployment

output are central to the unemployment decomposition, however, and will be presented in detail. The basic neoclassical growth model assumes perfectly competitive markets for goods and productive services. Firms are price-takers, and they simultaneously choose labor input and product output so as to maximize expected profit. Labor supply is inelastic to the real consumption wage and increases over time at the rate of population growth. At any given time, perfectly flexible wages and prices adjust to equate labor supply and demand at the equilibrium real wage, so that full employment always prevails. A similar adjustment occurs in the capital market, with the real rental rate on capital services equilibrating the demand and supply of real capital. Hence, current savings are always invested and there is never a deficiency or excess of aggregate demand. The natural growth rate is governed by the rate of population growth and the rate of Harrod-neutral technical progress and is therefore completely supply determined. Changes in the saving rate can shift the level of growth path but cannot alter the natural growth rate. In contrast, the HC Model" allows for departures from the fullemployment growth path 'owing to gradual price adjustments. The key assumptions underlying this property are as follows. (1) Firms are imperfectly competitive and set prices as a markup over normal unit labor costs, with allowance for the prices of imported inputs and the current state of demand. The master price equation has the general form: P=P(ULC,PM,CU),

(12)

where P is product price, U LC is normal unit labor cost, based on a moving average trend of manhour productivity, PM is the price of imports, and CU is an index of capacity utilization. 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 nominal wages induced by shifts in aggregate demand, themselves induce price movements in the same direction, greatly mitigating the response of real wages to demand pressures in labor markets. In contrast, supply shocks which directly raise production costs, such as the energy shocks of the 1970s, have greater potential to alter real wage rates unless they are offset by prompt and substantial wage indexation. As a corollary to real wage inflexibility under markup pricing, macroeconomic models which incorporate the hypothesis generally depend for their equilibrating properties on absolute variations in the wage-price level, operating through the Phillips curve and markup mechanisms. In the ~The model is fully documented in Hickman and Coen (1976) and Coen and Hickman (1980a, 1980b,198Oc,1983,1984).

E.G. Hickman, Real wages, aggregate demand, and unemployment

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standard textbook IS-LM model, for example, restoration of long-term equilibrium after a shock depends on price-induced changes in the real money supply and interest rates." In some of the larger econometric models, real wealth arguments in the aggregate demand functions are also involved." In either event, the equilibrating mechanism operates largely through the transactions or wealth effects of price-level changes rather than through relative prices as in the perfectly competitive classical model. (2) Given prices, output is determined by effective demand, which is disaggregated into three categories of investment, six of consumption, federal and state and local purchases, exports, and imports. These are dynamic demand functions, with lags introduced by capital stock adjustment processes; price, wage and output expectations; permanent income considerations; and adjustment costs. The income and expenditure sides are linked by corporate saving and dividend equations and a disaggregated model of taxes and transfers. (3) Firms choose capital and labor inputs to minimize cost, conditional on expected output and factor prices." The desired long-run or equilibrium inputs are derived by minimizing the cost of producing the expected output. Only part of the gap between actual and desired inputs is closed each year, however, owing to adjustment costs, so that the short-term factor demand functions contain lags which may prevent the attainment of full long-term equilibrium inputs for the given level of production. The general form of the labor demand function is MH=MH(WEfQE,XE,MH(-I)),

(13)

where M H is manhours, WE/QE is the expected wage-rental ratio, X E is the expected level of aggregate output, and manhours enter with a lag to reflect adjustment costs. There is a similar expression for the desired stock of capital, which provides the demand function for business fixed investment. (4) Labor force participation is a function of the real after-tax consumption wage and the ratio of employment to population [Coen and Hickman (1980a)]. The latter variable is included to capture the 'discouraged worker effect', a non-price signal which induces potential workers to withdraw from the labor market when unemployment rises. The labor force participation model is disaggregated into 16 age-sex groups, so that the aggregate labor 6See, for example, Dornbusch and Fischer (1984), Gordon (1984), and Hall and Taylor (1985). 7The equilibrating mechanisms in u.s. econometric models are discussed in Hickman (1984) and those in empirical multinational models in Hickman (1986). 8The cost-minimization assumption is not common among econometric models. Of the 14 models included in a simulation study of the macroeconomic impacts of energy shocks [Hickman (1984)], only 3 U.S. models - Hickrnan-Coen, Michigan Annual, and Mork - and the MACE model for Canada included the real wage as an argument along with output in the labor demand function.

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B.G. Hickman, Real wages, aggregate demand, and unemployment

force depends on the composition of population as well as its level. The labor supply function may be written schematically as L=L(WATjPC,E,NNI),

(14)

where L is the civilian labor force, W A T is the nominal after-tax wage rate, PC is the consumer price deflator, E is civilian employment, and N N I is the non-institutional population 16 years and over. Average hours, AH, are explained in a separate equation by the unemployment rate, the after-tax real wage rate, and the proportion of women in the labor force. (5) The complete model also includes an 'expectations-augmented' Phillips curve of the form: DW=DW(U -UF,DPC( -1)),

(15)

where DW is the rate of change of nominal wages, (U - U F) is the gap between the actual and natural unemployment rates, and DPC( -1) is the lagged rate of consumer price inflation. Since this paper is not concerned with inflation-unemployment trade-offs or the determination of the absolute level of wages and prices, neither the wage equation (15) nor the price equation (12) is operational in the subsequent analysis, which depends only on real wage rates. (6) The model can be solved for potential as well as actual output. Potential GNP is defined as that output which would be realized each year if the markets for labor and capital were continuously cleared at the natural rate of unemployment [Coen and Hickman (1980b)]. A key characteristic of this concept is that potential output is unaffected by deviations of actual output, factor inputs, and real factor prices from their full-employment values. It is truly a measure of productive potential in which output is constrained only by available technology and factor supplies, and labor and capital are assumed to be fully employed each period along the growth path. Departures from the natural path imply disequilibrium in the factor markets, as the quantities of capital and labor deviate from their full-employment levels, but these temporary deviations do not affect potential output in subsequent periods, since they can be offset by future changes in investment and employment.

4. The labor market The explicit equation structure of the labor supply and demand blocs and the derivation of potential output in the HC Model are described in this section.

B.G. Hickman , Real wages, aggregate demand, and unemployment

1539

4.1 Labor supply The model contains labor-force participation equations for 16 age-sex groups, of the form:

+a4,;{WATIPC)I+aS.iAH,+a6.it+a,.iNNIM ,],

(16)

where L, is the labor force and N N I, the population in the ith group, E is aggregate employment, N N I is the non-institutional population 16 years or older, LA is the number of persons in the armed forces, W A T is the after-tax wage rate, PC is the implicit deflator for consumer goods, AH is aggregate average hours of work, t is a time index, and N N I M is the ratio of males aged 16-34 to those 35-64. The ratio EI N N I captures the discouraged worker effect, whereas N N I M is included in the female participation equations only, in conformity with the hypothesis that increases in this ratio affect the participation rates of younger women positively and of older women negatively [Easterlin (1978)]. The single equation for average hours takes the form:

where AH is average hours per year, U is the unemployment rate , and LWis the proportion of women aged 20 and over. Workers' desired hours are assumed to depend on the wage rate, but cyclical variations in labor demand, proxied here by the unemployment rate, may affect actual hours. Average hours may also vary inversely with the proportion of women in the labor force, since they are more likely to engage in part-time work. The labor supply model is completed by summing over the relevant agesex participation equations to obtain Land LW: 16

L,== L t.;

(18)

i= 1

16

L l¥, ==

L LillL,. i= 11

(19)

4.2. Labour demand The demands for labor and capital are interrelated in the model , since they are jointly derived on the assumption that firms minimize production costs subject to a long-run or planning Cobb-Douglas production function with

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B.G. Hickman, Real wages. aggregate demand, and unemployment

constant returns to scale: (20) where X N R* is expected output, K* is desired business fixed capital stock, M H* is desired manhours, and p is the rate of neutral technical progress. Minimizing the production cost function,

C{XNRi) = Q,*K: + W:MH:,

(21)

subject to (20) gives the long-run factor demand functions: (22) and (23) 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 defined by Q=PI(r+d)T, where PI is the investment price deflator, r is the after-tax rate of return, assumed to be constant at 6 percent, d is the depreciation rate, and Tsymbolizes the tax treatment of investment expenditure. Adjustment costs prevent firms from accommodating immediately to variations in the desired inputs. These adjustment costs include external purchase costs and internal installation costs for capital goods and hiring, training. and layoff costs for labor. They are represented implicitly by exponential partial adjustment processes: (24)

(25) where f and g are the adjustment speeds for labor and capital. Combining the desired input and adjustment hypotheses yields the shortterm or disequilibrium demand functions:

MH,== {[a/{l-a)] -"A -l[{W*/Q*),raXNR: e-P'}!MH,l_-/,

(26)

= {[a/(I-a)]I-" A -l[(W*/Q*),]I-aXNR: e- P'}9K,l.:!.

(27)

K,

Joint estimation of the short-run demand functions (26) and (27) yields estimated values of the adjustment speeds, f and g, and of the structural parameters of the production function (20) and long-run factor demand

B.G. Hickman, Real wages, aggregate demand, and unemployment

1541

fumctions (22) and (23). With regard to expectations, extensive testing of adaptive schemes resulted in the choice of a second-order a utoregression for PI*, the only expectational component of Q*, and a first-order autoregression for X N R* which, however, differed so little from actual X N R that equality between actual and expected output was assumed in the final estimates. The expected wage is determined from the wage equation (15), assuming that agents know the Phillips curve and estimate lV on the basis of the unemployment gap observed in the previous period. 4.3. Labor market identities

The following identities complete the labor market model:

EP,:: M H,fAH"

(28)

where EP is private employment,

E,:: EP, + EG"

(29)

where EG is government employment, an exogenous policy variable, UN,::L,-E"

(30)

where UN is the number of unemployed persons, and U,::UN,fL"

(31)

where U is the unemployment rate. For expositional simplicity, the subsequent analysis will suppress the dist inction between manhours and the number of employees and between private and government employment, proceeding as if all employment were private and average hours were constant, so that the labor demand function can be regarded as referring directly to total employment instead of to private manhours. The empirical measures do, of course, take account of the variations in average hours and public employment, but the effects are small enough to be safely neglected. 4.4. Short-run disequilibrium

A short-run disequilibrium is determined each period in the simultaneous solution of the labor market equations. Firms are not in long-run equilibrium because adjustment costs keep them off their planning production function in the short run. Neither is there continuous market-clearing, since

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B.G. Hickman, Real wages, aggregate demand, and IInemployment

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. To measure the extent of classical and Keynesian unemployment, it is necessary to determine potential output and the full-employment real wage. 4.5 Full-employment labor slIpply

The first step is to specify the natural unemployment rate in order to estimate the full-employment labor supply. The concept in the He Model follows Wachter (1976) in the method of accounting for the effects of changes in the age-sex composition of the labor force on structural unemployment. The demographic shift toward younger workers from the mid-fifties to the mid-seventies increased the importance of age groups with persistently high unemployment rates. Moreover, minimum wage legislation prevented adjustments in demand favoring untrained and lower-skilled young workers and unemployment insurance reduced the cost of unemployment so that structural and frictional unemployment rose among secondary workers, further increasing their already high unemployment rates. Thus, some increase in the aggregate unemployment rate consistent with a given degree of labor market tightness and nominal wage pressures is to be expected from these demographic influences. The basic assumption in estimating the natural rate is that prime-age male workers were largely unaffected by these labor market developments, so that their unemployment rate in a benchmark year can be interpreted as a specific full-employment unemployment rate which does not change over time and therefore can be used to isolate that portion of the change in unemployment rates of the other age-sex groups which is structural rather than cyclical. The natural unemployment rate is calculated as a weighted average of the natural rates for the 16 age-sex groups: 16

UF,=

L UFi,(LF;,/LF,),

(32)

i;1

where V F i is the full-employment unemployment rate and LF i the fullemployment labor force in the ith age-sex group. The V F i, are based on the following regressions: (33)

where Vi is the actual unemployment rate in the ith group, V p is the unemployment rate in the prime-age male group (45-54) and the other variables are as previously defined. Thus cyclical variations in the age-sex

B.G. Hickman, Rea/wages, aggregate demand, and Imemp/oymellt

1543

specific unemployment rates are related to cyclical variations in V p' whereas structural shifts in the Vi over time are related to the share of the ilh group in- the total population. The full-employment unemployment rate for primeage males, V F pI' is held constant at its 1956 level of 3.0 percent, and the other V F il are estimated by setting V pI = 3.0 in eq. (33) and calculating the value of the right-hand side. It is important to emphasize that V F is not a non-accelerating inflation rate of unemployment (NAIRU), since it is not calculated from a Phillips curve by imposing the non-acceleration constraint. It does take account of changes over time in factors affecting structural and frictional unemployment, and the related changes in labor market tightness, but it does not impose the assumption of a vertical long-run Phillips curve. All the ingredients are now in place to solve for the full-employment labor supply conditional on the real wage rate. This may be seen by setting L il=LFil in (16), (18), and (19), and similarly setting E" AH" V" UY" L I, EP I, MH I, Vi' and VN I equal to their full-employment equivalents in (16), (17), (18), (19), (28), (29), (30), (31); (32) and (33). These equations can then be solved simultaneously for the natural unemployment rate, V F, and the corresponding full-employment supply of manhours, M H F, conditional on given values of the real wage, the population and its age-sex distribution, and the size of the armed forces, LA, and government employment, EG. 4.6. The natural growth path

Along the natural growth path of potential output both labor and capital are fully employed. Making use first of the labor market condition, potential output is defined as the level of output that would equate labor supply and demand at the natural rate of unemployment and full-employment wage rate. Since the labor demand function (26) relates manhours to output and - relative factor prices, an expression may be derived for potential output, conditional on the wage-rental ratio, by substituting M H F for M Hand solving the equation for output:

where X N RP is potential output. Since full employment would prevail each period along the natural growth path, note that X N RP depends on M HF in the current and preceding year (and hence on all previous years since the path was established), irrespective of whether the economy actually operated at full employment in the preceding year. The expected relative factor price ratio in (34) is W*/Q* == (W*/ P 1*) [(d+r)n - 1 • Thus, to implement (34) historically, actual wages and prices could be used, along with the model equations relating actual and expected

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E.G. Hickman, Real wages, aggregate demand, and unemployment

wages and prices, to estimate W*/PI* and W*/Q*. Observed wages and prices are affected by cyclical fluctuations about the natural growth path, however, so that it is inappropriate to use them in its construction. It is assumed instead that the real product wage grows at the same rate as potential labor productivity along the natural path:

(W/P>r!UV/P)/-l =(XNRP/MHF)r!(XNRP/MHF)/_l'

(35)

This assumption is not only observationally realistic but also consistent with the overall structure of the model. Nominal wages and prices are endogenous in the complete model, but prices are related to unit labor cost with a constant long-term markup, implying constant factor shares in long-run equilibrium and equality of the growth rates of the real wage and labor productivity. The real wage in the labor demand function is in terms of capital goods prices and that in the labor supply equations in terms of consumer prices, but the differential trend of consumer and capital goods prices is negligible for present purposes and may be ignored, setting (W/P) = (W/PI) in (35) and correcting (W/PC) for taxes to derive (WAT/PC) in (16) and (17). Finally, assuming that real wage expectations would be realized along the natural growth path, (36)

where the last term is an autonomous component of (W/Q*), since d and r are known and only changes in T which are unanticipated and permanent are assumed to affect the equilibrium capital-labor ratio. Hence, the equilibrium wage-rental ratio increases at the same rate as labor productivity and the real wage along the natural path." Rewriting (34) in productivity form as (X NRP/M HF)/= B[W*/Q*)/)7eP/(MHFr!MHF/_ 1 ) ( 1 -

1)/1,

(37)

where B=A[(l-cc)/ccr"', and using (16)-(19), (28)-(33), (35)-(37), and the identity (38) X N RP, = M HFlXN RP/M HF)/ 9An exogenous change in the wage-rental ratio cannot be directly captured in this framework. In the case of the first oil shock, for example, the pass-through of higher oil prices into higher prices of final goods sharply reduced (IV/PI) relative to the pre-existing path. The wage-rental ratio for 1974-1975 was adjusted downward accordingly in the natural growth path solution, leading to a permanent reduction in the level of potential output. [For further discussion of the impact of energy shocks as measured in the model, see Coen and Hickman (1983).] Other exogenous shocks may also affect the factor-price ratio and potential and actual output. Thus, the depreciation incentives in the 1981 tax legislation are estimated to have reduced the rentalwage ratio sufficiently to increase the level of potential output, but not the long-run growth rate, by about one percent in the 1980s [Co en and Hickman (1984)].

B.G. l1ickman, Real wages, aggregate demand, and unemployment

1545

we can solve simultaneously for the full employment values of labor productivity, output, labor force, employment, unemployment, hours of work, and the real wage and rental-wage ratio along the natural growth path, for exogenous values of the demographic and policy variables (population, armed forces, government employment, and tax parameters). Capital as well as labor must be fully employed along the natural growth path. In the standard neoclassical model, a constant fraction of output is saved and automatically invested . In contrast, the HC Model includes an explicit investment demand function, eq. (27), which determines actual business fixed investment, and saving need not equal investment ex-ante. Eq . (27) may be used to determine the path of full employment business fixed capital stock, however, by setting current and lagged capital stock and current output equal to their full employment values KF" KF/_ 1 , and X N RP,. With the revised eq. (27) and the identity relating gross investment and capital stock,

IF,=KF,-(l-d)KF,-l>

(39)

added to the earlier equation systems, the net and gross business fixed investment required to sustain the natural growth path are fully determinate. A greater flow of saving could not be profitably absorbed in business fixed capital formation under the given investment conditions, and a smaller flow would be inadequate to attain the required rate of capital deepening to equilibrate the capital-labor and rental-wage ratios. To expand on the last statement, the optimality condition in the factor demand system equates the marginal rate of substitution to the expected wage-rental ratio, so that in the absence of adjustment lags,

K*/MH* =(a/l-a)(W*/Q*)=(a/l-a)(W*/PI*)[(r+d)Tr I.

(37)

As the real wage rises over time with productivity growth, labor becomes increasingly expensive relative to capital, encouraging continuous capital deepening. According to the econometric evidence in Coen and Hickman (1980c), the desired rate of return r used in fixed business investment decisions does not fluctuate with nominal or real interest rates or equity yields, and it is held constant at 6 percent after taxes in the model. The real rate of return to capital has remained constant because firms have not absorbed more saving for purposes of business fixed capital formation than was consistent with maintenance of the required rate of return, and the surplus saving has gone into residential construction, inventory accumulation, or net foreign investment. To summarize, simultaneous solution of eqs. (16)-(19), (27)-(33), and (35)-(39), provides consistent estimates of potential output and the full-

1546

B.G. Ilickman, Real wages, aggregate demand, and lInemployment

employment magnitudes of the labor force, employment, average hours, real wage, wage-rental ratio, and capital stock, for given values of the demographic and policy variables. The estimates of the full-employment wage rate, labor force, employment and hours are used in the following analysis of Keynesian and classical unemployment. 5. The conceptual framework In order to distinguish between the impacts of high real wages and deficient effective demand on unemployment, the actual supply and demand functions for labor must be compared with their full-employment counterparts. Some complications associated with the carryover effects of lagged disequilibrium in the labor market will be neglected at first. The theoretical development will also abstract from expectational errors by assuming perfect foresight on the real wage. It will be shown subsequently that expectational errors are normally of secondary importance for the empirical estimates. The conceptual framework is illustrated in fig. 1, in which the real wage is measured vertically and the quantity of employment horizontally. The shortrun labor demand function is labeled LD, and its position depends on the quantity of current output and on lagged employment and other variables as discussed above. At the current real 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 magnitude of the estimated elasticity of labor force participation in the He Model. Its position depends on the level and age-sex distribution of the population, and also on the level of E, owing to the discouraged worker effect on labor force participation. The number of unemployed workers is given by UN=(L-E). The full employment labor force is LF, and EF is the corresponding 'fullemployment' volume of employment, equal to (LF - UN F), where UNF is

lD

UP

¥R

~RF

...------t-;--------+----1t---"----t

EA

EF

Fig. 1

l LA

IF

B.G. Hickman, Real wages, aggregate demand, and unemployment

t547

the number of persons who would be unemployed at the natural rate of unemployment, UFo The labor demand function at potential output is LDP, and WRF is the real wage rate which would clear the labor market, except for natural unemployment, if output were at its potential level. As discussed above, all these full employment functions and magnitudes are simultaneously determined in the solution for the natural growth path. Suppose now that the real wage were reduced to WRF while aggregate demand and output remained unchanged. The level of employment under this hypothetical experiment would be EA. Thus, of the total shortfall of employment, EF - E, an amount EA - E is attributable to the wage gap WR - WRF. The remainder, EF - EA, stems from the deficient effective demand for output. The employment shortfall may therefore be decomposed into its wage and demand components: EF -E=(EA-E)+(EF -EA).

(40)

At the prevailing wage, excess unemployment exists, amounting to UNUN F. The excess may be "decomposed in two ways. First, since UN - UNF=(L-E)-(LF-EF)=(EF -E)-(LF -L),

(41)

the excess is smaller than the employment shortfall by the amount of 'hidden' unemployment, LF - L. The hidden unemployment is due, of course, to the induced withdrawal of potential workers from the labor force because of a perceived lack of job opportunities at the current employment level. Second, the excess unemployment may also be factored into a wage component equal to UN - UNA and a demand component given by UNA - UNF, corresponding to the associated employment shortfalls: UN - UNF=(UN - UNA)+(UNA- UNF).

(42)

The demand component has the following interpretation. Under the hypothetical wage reduction, the increase of employment to EA would induce an increase of the labor force to LA, owing to the diminished discouraged worker effect. This would result in hypothetical excess unemployment equal to UNA- UNF=(LA-EA)-(LF -EF)=(EF -EA)-(LF -LA).

(43)

Thus, the demand component of total excess unemployment consists of the residual employment shortfall less the residual volume of hidden unemployment. The smaller employment shortfall at the reduced real wage would be partly offset by the induced reduction of hidden unemployment.

1548

B.G. Hickman, Real wages, aggregate demand, and unemployment

This demand component would exist even if the real wage were at the full employment level. Since it reflects deficient demand in the product market, it represents the Keynesian component of excess unemployment. Correspondingly, the wage component measures the extent of classical unemployment due to an excessive real wage rate.

Employment dynamics and carryover unemployment It might be thought that the demand component of the employment shortfall, EF - EA, would necessarily be zero when actual and potential output were equal. This is not generally true, however, since equality of actual and potential output does not imply that the actual demand function for labor LD coincides with the full-employment demand schedule LDP. Both shedules depend on lagged employment, but this is measured by EF( -1) instead of E( -1) in the full-employment case, since the natural growth path is defined for a condition of continuous full employment. Thus, LD will coincide with LDP only if actual and potential output are equal and labor was fully employed in the preceding period. Fig. 2 illustrates the situation when a shortfall of actual output this period follows upon excess unemployment in the preceding period. This would occur, for example, if output and employment fell below their fu1lemployment levels in period t - 1 and output recovered only partially in period t. The actual and full-employment demand and supply schedules and the associated quantities are the same as before. The new schedule, LDB, is hypothetical and shows the demand for labor which would exist if actual output were at the potential level, given the actual employment of the preceding period. The distance EF - EB measures the carryover component

I LD

LDt

I

lDl'

I I I

I

IIR

I I I

I

!jAF

I I I

I £A

£8

Fig. 2

£F

l LA

u

LF

B.G. Hickman, Real wages, aggregate demand, and unemployment

1549

of the total employment shortfall EF - E. It is the residual shortfall which would persist even if actual output and the real wage were both at their fullemployment levels in period t, owing to the drag exerted by the employment shortfall EF - E in period t - 1. If carryover unemployment is recognized as a separate category, the employment shortfall may be decomposed into three elements: EF -E=(EA-E)+(EB-EA)+(EF -EB).

(44)

In this formulation, EB - EA measures the employment· shortfall due to an output gap, just as EA - E measures that due to a wage gap. In the illustrative example, the output gap is negative (Y < YP) and the wage gap positive (WR > W RF), but the gaps may go either way in principle and the output gaps are frequently negative in the empirical estimates. The corresponding breakdown of excess unemployment is given by UN - UNF=(UN - UNA)+(UNA-UNB)+(UNB- UNF),

(45)

where UNB = LB - EB and the other terms were defined earlier. These three-fold decompositions are interesting and meaningful, and empirical estimates based on (44) and (45) are provided below. The two-fold breakdowns given by (40) and (42) are preferred, however, on the grounds that the contribution of deficient aggregate demand to excess unemployment should be measured by the gap between actual output and that output which would be required to achieve full employment of labor if the real wage were at the full-employment level, rather than by the gap between actual and potential output. In the case illustrated by fig. 2, this would require a positive output gap. On this interpretation, the volume of Keynesian unemployment includes the carryover component and is measured by UNA - UNF rather than UNA - UN B. In the sequel, EB - EA and UNA - UNB will be called output (gap) components to distinguish them from the demand components EF - EA and UNA - UNB which include the carryover terms. The concepts of actual, natural, excess, hidden, demand gap or Keynesian, and wage gap or classical, unemployment are reasonably well defined in this framework. The distinction often made between voluntary and involuntary unemployment is more problematic, however. If natural unemployment were considered to be completely voluntary - on the basis of search theoretic considerations, for example - EF would be the appropriate benchmark and the entire employment shortfall, EF -E, would be involuntary, with corresponding classical and Keynesian components. On this interpretation, only excess unemployment, UN - UNF, is involuntary. If job search is thought to be a minor determinant of unemployment, on

1550

B.G. Hickman, Real wages, aggregate demand, and unemployment

the other hand, natural unemployment should be classified as involuntary, on the grounds that individuals are still being rationed out of the labor market when E = EF, even if EF is a reasonable 'full-employment' target for the society as a whole. Even so, the upper limit for involuntary unemployment would not be LF, but rather L or LA, if, as seems appropriate, hidden unemployment is considered to be voluntary.'? On these assumptions, involuntary unemployment either exceeds (LA - E) or equals (L- E) observed unemployment, rather than being confined to excess unemployment. Since natural unemployment probably contains both voluntary and involuntary components, it may not be appropriate to identify involuntary unemployment either with excess unemployment or the quantity of nonhidden unemployment, or to label the wage and demand components of either measure as involuntary classical and Keynesian unemployment.

6. Methodology Estimates are required of the full employment and hypothetical magnitudes in figs. 1 and 2. The full-employment estimates have already been described. The hypothetical values of employment, unemployment, and labor force were obtained by simulation methods, using the labor market blocs of the He Model. To calculate EA 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 fullemployment values of the real wage rates entering labor demand and supply. The estimates of EB and LB were obtained from a similar simulation with output as wel1 as real wages at the full-employment level. The remaining question is whether the hypothetical and ful1-employment simulations should be compared with the actual data on employment, unemployment, and labor force, or whether model solutions for these variables should be used instead. It was decided to base the comparisons on the model predictions from a simultaneous solution of the labor market blocs rather than on the historical data, so as to purge the calculated shortfalls of stochastic errors. Notice that these are partial equilibrium results. No allowance is made for a feedback from the altered values of labor market variables to aggregate demand and output. This is the appropriate procedure for measuring the wage and demand components of unemployment, but not for investigating the consequences of an exogenous reduction of real wage rates for the economy as a whole. 'O'fhe choice between L or LA depends on whether the voluntary hidden unemployment is evaluated at WR or WRF. The latter choice is preferable conceptually, since the size of LF itself depends on the full employment wage WRF.

1551

E.G. Hickman, Real wages, aggregate demand, and unemplo}-ment

7. Output, unemployment and real wage history

It is useful to observe the history of actual and potential GNP, unemployment, and real wages before examining the unemployment decompositions. For this purpose use is made of the actual data on the real wage and unemployment rather than the simulated values underlying the subsequent analytical decompositions. As shown in table 1, the economy seldom operated at its potential level during 1959-1982, exhibiting instead varying periods of under- and overutilization as measured by the ratio of actual to potential output. The doldrums of the early sixties were succeeded by the Vietnam era of low unemployment and high utilization. The economy did not stray far from potential during 1970-1972, but utilization exceeded potential by 2 percent in 1973, before declining in 1974-1975 to a low of 96 percent following the oil shock. The subsequent recovery carried the utilization rate to 103 percent during 1978-1979, before it again declined to a 20-year low of 95 percent in 1982. During the 1960s, unemployment exceeded the natural rate whenever actual output fell below potential, and vice versa, as may be seen by Table 1 Output, unemployment, and real wages. 1959

1960

Actual and potential G:-;P 721.7 Actual 6.0 Potential 734.8 3,9 98.2 ACT/POT Actual and natural Actual Natural ACT-NAT

1961

1962

(billions or 1972 dollars) 737.2 756.6 800.3 2.1 2.6 5.8 765.7 790.4 819.6 4.2 3.2 3.7 96.3 95.7 97.6

unemployment rates (percent) 5.47 5.53 6.69 5.54 4.38 4.46 4.53 4.55 1.09 1.07 2.16 0.99

1963

832.5 4.0 851.5 3.9 97.8

1964

876.4 5.3 888.5 4.3 98.6

1965

1966

929.3 6.0 921.2 3.7 100.9

9848 6.0 941.1 2.2 104.6

1967

1968

1969

1970

1011.4 2.7 978.0 3.9 103.4

1058.1 46 1019.8 4.3 103.8

1087.6 2.8 1053.6 3.3 103,2

1085.6 -0.2 1078.8 2.4 100.6

5.67 4.71 0.95

5.18 4.90 0.28

4.52 5.08 -0.56

3.79 5.25 -1.46

3.85 5.31 -1.47

3.58 5.39 -1.81

3.51 5.50 -1.99

4.94 5.65 -0.70

Actual and potential real wage (1972 dollars per hour) 3,29 Actual 3.39 3.68 3.77 3.53 3,32 3,62 3.42 3.50 3.74 Potential ACT/POT 99.0 99.0 100.8 101.6 100.9

3.92 3.87 101.3

4.06 3.98 102.0

4.26 4.02 105.9

4.34 4.15 104.6

4.51 4.28 105.5

4.64 4.35 106.7

4.70 4.39 107.1

1971

1972

1973

1974

Actual and potential GNP (billions or 1972 dollars) Actual 1122.4 1185.9 1254.3 1246.3 3.4 5.7 5.8 -0.6 1261.4 Potential 1125.6 1189.3 1232.5 5.7 4.3 3.6 2.3 ACT/POT 99.7 99.7 101.8 98.8 Actual and natural unemployment rates (percent) 4.88 5.61 Actual 5.94 5.61 Natural 5.81 5.91 5.98 5.99 ACT-NAT -0.30 -1.10 -0.38 0.13

1975

1976

1977

1978

1979

1980

1981

1982

1231.6 -1.2 1279.8 1.5 96.2

1298.2 5.4 1327.4 3.7 97.8

1369.7 5.5 1362.7 2.7 100.5

1438.6 5.0 1399.5 2.7 102.8

1479.4 2.8 1440.6 2.9 102.7

1475.0 -0.3 1473.3 23 100.1

1513.8 2.6 1535.9 4.3 98.6

1485.4 -1.9 1571.2 2.3 94.5

8.46 6.05 2.41

7.70 6.07 1.64

7.06 6.05 1.01

6.07 6.00 0.07

5.85 5.94 -0.09

7.14 5.86 1.28

7.61 5.75 1.87

9.69 5.58 4.11

Actual and potential real wage (1971 dollars per hour) 4.83 4.93 Actual 4.74 5.03 4.68 4.52 4.67 4.73 4.64 4.41 Potential 104.9 103.3 106.2 106.2 106.2 ACT/POT

4.81 4.47 107.5

4.91 4.47 109.7

4.98 4.48 111.2

5.05 4.51 111.9

5.12 4.53 112.9

5.16 4.64 111.2

5.32 4.68 113.8

1552

E.G. llickman, Real wages, aggregate demand, and unemployment

comparing the top and middle panels of table 1. This is not a necessary outcome under the Hickman-Coen concept of the natural growth path of potential output, however, in contrast to other constructs which assume competitive markets for goods and services either explicitly or implicitly and which allow past shortfalls to affect the current level of potential output. Under competitive conditions, if actual unemployment is at the natural rate, actual output must necessarily be at the full employment level. This is 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 output resulting from a cleared labor market is therefore by definition at the full-employment level. With price-setting firms and imperfect markets, however, labor demand is conditional on output, which is demand-determined in product markets. Unemployment may therefore exceed the natural rate even with output at its potential level, if the real wage is above the level which would prevail if the labor market were to be cleared at potential GNP, or if carryover unemployment exists because of a preceding shortfall. . Such excess unemployment actually occurred with the economy slightly above potential in 1977 and 1980. This could occur during those years because the real wage gap, WRjWRF, was positive and large (see the lower panel of table 1).11 Of course, effective demand may also on occasion offset the adverse effects of a wage gap, as it did in 1978-1979, when despite a large wage gap, unemployment was reduced to the natural level by high effective demand as reflected in a utilization rate of 103 percent. The wage gap was small or negative during the early 1960s, so that classical unemployment could not - have been an important problem. The wage gap rose to successively higher plateaus during the Vietnam War years and in the mid-1970s, however, increasing its unemployment impact. To judge its relative importance, the remaining task is to quantify the contributions of the classical and Keynesian components of unemployment during 1959-1982. 8. Sources of unemployment The proximate sources of excess unemployment are quantified in table 2, which reports the measures and decompositions which were defined in fig. 1. The natural level of unemployment rose from about 3 million workers in 1959 to more than 6 million in the last half of the 1970s. The estimated excess of actual over natural unemployment was positive in the first half and negative in the second half of the 1960s. Excess unemployment was also negative during 1971-1973 and 1978-1979, but it was positive in 1974-1977 "Carryover unemployment also contributed 10 the excess, as will be shown below in table 5, but it was less important than the real wage gap.

B.G. Hickman, Real wages,· aggregate demand, and unemployment

1553

and again in 1980-1982. The worst year by far was 1982, when the excess over natural unemployment is estimated at 4.3 million. Employment was below its natural level (the shortfall was positive) during all but the Vietnam War years 1966-1969 and in 1979 (see the third panel of table 2). This can be a seriously misleading measure of the unemployment problem, however, because of hidden unemployment. As shown in the second panel, the volume of hidden unemployment is often substantial, so that elimination of the employment shortfall would reduce unemployment by a considerably smaller amount. Table 2 Components of unemployment (millions of persons). 1959 1960

1961

1962 1963 1964 1965

Unemployment: Excess= actua1- natural 1.21 1.26 1.35 1.10 0.82 0.42 Excess Actual 4.23 4.39 4.59 4.38 4.27 4.07 Natural 3.02 3.13 3.23 3.28 3.45 3.65 Unemployment: Excess= shortfall- hidden 1.21 1.26 1.35 1.10 0.82 0.42 Excess Shortfall 1.34 1.81 2.17 1.88 1.89 1.39 Hidden 0.14 0.56 0.81 0.78 1.07 0.98 Employment: Shortfall and components Shortfall 1.34 1.81 2.17 1.88 1.89 1.39 Wage -0.20 -0.15 -0.08 -0.12 0.06 -0.11 Demand 1.54 1.97 2.24 2.00 1.84 1.51 Unemployment: Excess and components 1.21 1.26 1.35 1.10 0.82 0.42 Excess Wage -0.06 -0.Q3 -0.01 -0.Q3 0.10 -0.05 Demand 1.27 1.29 1.37 1.13 0.72 0.47 1971

1966 1967 1968 1969 1970

-0.45 -1.57 -1.14 -1.51 -1.36 -0.67 3.41 2.47 3.02 2.79 3.13 4.05 3.86 4.04 4.16 4.30 4.49 4.72 -0.45 -1.57 -1.14 -1.51 -1.36 -0.67 0.50 -0.96 -0.42 -1.00 -0.51 0.49 0.95 0.61 0.72 0.51 0.84 1.16 0.50 -0.96 -0.42 -1.00 -0.51 0.05 0.22 0.25 0.04 0.32 0.44 -1.18 -0.66 -1.04 -0.84

0.49 0.39 0.10

-0.45 -1.57 -1.14 - L51 -1.36 -0.67 0.08 0.25 0.35 0.18 0.45 0.49 -0.53 -1.83 -1.49 -1.69 -1.81 -1.16

1972 1973 1974 1975 1976 1977 1978 1979 1980 1981

Unemployment: Excess= actual-natural -0.02 0.Q7 -1.02 0.42 1.69 1.30 0.44 Excess Actual 4.97 5.32 4.44 6.02 7.49 7.26 6.53 Natural 5.00 5.25 5.46 5.60 5.80 5.96 6.09 Unemployment: Excess= shortfall- hidden Excess -0.02 0.07 -1.02 0.42 1.69 1.30 0.44 Shortfall 1.22 1.65 0.39 2.55 4.25 3.38 2.06 Hidden 1.24 1.58 1.41 2.13 2.56 2.08 1.62 Employment: Shortfall and components Shortfall 1.22 1.65 0.39 2.55 4.25 3.38 2.06 Wage 0.13 0.00 0.15 0.84 0.83 -0.47 0.45 Demand 1.10 1.65 0.24 1.70 3.42 3.85 1.61 Unemployment: Excess and components Excess -0.02 0.07 -1.02 0.42 1.69 1.30 0.44 Wage 0.32 0.26 0.32 0.84 0.75 -0.10 0.59 Demand -0.34 -0.18 -1.34 -0.42 0.94 1.41 -0.15

1982

-0.35 -0.37 5.82 5.89 6.18 6.26

1.01 7.32 6.31

2.29 4.20 8.61 10.43 6.32 6.24

-0.35 -0.37 0.57 0.07 0.92 0.44

1.01 1.73 0.72

2.29 3.28 1.00

4.20 6.30 2.11

0.57 0.07 0.46 0.52 0.11 -0.45

1.73 0.64 1.10

3.28 0.51 2.77

6.30 0.37 5.93

-0.35 -0.37 0.70 0.81 -1.06 -1.19

1.01 0.88 0.13

2.29 0.75 1.53

4.20 0.57 3.63

1554

B.G. Hickman, Real wages, aggregate demand, and unemployment

The employment shortfall is factored into its wage and demand (classical and Keynesian) components in the third panel, and excess unemployment is similarly decomposed in the final panel. The results confirm that the wage component of unemployment rose from negligible amounts in the early 1960s to moderate levels in the Vietnam years and the early 1970s and larger heights thereafter. It was the dominant source of excess unemployment in 1974, 1977, and 1980. The demand component was the major depressant during 1975-1976 and 1981-1982, when excess unemployment was especially large. Finally, high effective demand overwhelmed the effects of high real wages during 1978-1979, as unemployment fell below the natural level for the only period between 1974 and 1982. The magnitude of the wage component depends on the wage elasticity of labor demand as well as on the size of the wage gap. Given a Cobb-Douglas technology and assuming that adjustment costs keeps firms off the long-run production function, the short-run elasticity of manhour input 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, IX, and the adjustment speed of labor input, f The estimated values of these parameters from eq. (26) are 0.25 and 0.65, respectively, yielding an estimated wage elasticity for manhours of 0.16. The elasticity for employment alone, after allowing for induced changes in average hours, barely exceeds 0.1. This smaIl elasticity clearly restricts the potential scope of wage gaps as a cause of excess unemployment. 12 To some up, these new measures identify demand fluctuations as the major source of cyclical variations of unemployment about its natural level in the United States. The real wage gap has increased in importance, especially since 1974, but aggregate demand has remained the dominant determinant except in isolated years. 8.1 Effects of expectationol errors

The measures in table 2 are for labor demand as determined by eq. (2) on the basis of the expected real wage. Would the estimates of excess unemployment and its components differ substantially if perfect foresight on the real wage were assumed instead? In other words, to what extent do expectational errors affect the estimated wage gaps and the employment predictions of the model? To answer this question, the simulations were repeated with the actual real wage substituted for its expected value on the labor demand function and with all other variables as before. The results are shown in table 3 and it is apparent that the estimates of excess unemployment and its classical 12The elasticity of employment with respect to the real wage would be much larger (lJcr instead of a) under perfectly competitive conditions with firms on their short-run notional supply schedules, but this is an implausible behavioral hypothesis for the reasons discussed earlier.

B.G. Hickman, Real wages, aggregate demand, and unemploymclll

1555

Table 3 Components of unemployment (perfect foresight assumption) (millions of persons). 1959 1960 1961

1962

1963 1964 1965 1966 1967

Unemployment: Excess == actual- natural Excess 1.26 1.29 1.45 1.23 0.77 Actual 4.28 4.42 4.69 4.50 4.22 Natur al 3.02 3.13 3.23 3.28 3.45 Unemployment: Excess == shortfall- hidden Excess 1.26 1.29 1.45 1.23 0.77 Shortfall 1.42 1.86 2.30 2.05 1.82 Hidden 0.16 0.57 0.85 0.83 1.05 Employment: Shortfall and components Shortfall 1.42 1.86 2.30 2.05 1.82 -0.12 -0.10 0.06 0.05 -0.01 Wage Demand 1.54 1.97 2.24 2.00 1.84 Unemployment: Excess and component s Excess 1.26 1.29 1.45 1.23 0.77 Wage -0.01 0.00 0.08 0.10 0.05 Demand 1.27 1.29 1.37 1.1 3 0.72 1971

1968 1969

1970

0.54 -0.42 -1.53 -1.29 -1.41 -1.46 -0.81 4.19 3.44 2.51 2.87 2.89 3.02 3.92 3.65 3.86 4.04 4.16 4.30 4.49 4.72 0.54 -0.42 -1.53 -1.29 -1.41 -1.46 -0.81 1.55 0.53 -0.91 - 0.60 -0.88 -0.64 0.31 1.02 0.95 0.62 0.69 0.53 0.82 1.12 1.55 0.53 -0.91 -0.60 -0.88 -0.64 0.05 0.09 0.27 0.06 0.16 0.19 1.51 0.44 -1.18 -0.66 -1.04 -0.84

0.31 0.21 0.10

0.54 -0.42 -1.53 -1.29 -1.41 -1.46 -0.81 0.07 0.11 0.30 0.20 0.28 0.35 0.35 0.47 -0.53 -1.83 -1.49 -1.69 -1.81 -1.16

1972 1973 1974 1975 1976 1977 1978 1979

Unemployment: Excess =actual - natur al Excess -0.09 0.03 - 0.92 -0.03 1.28 1.87 0.45 -0.35 Actual 4.90 5.28 4.53 5.57 7.08 7.83 6.54 5.83 Natural 5.00 5.25 5.46 5.60 5.80 5.96 6.09 6.18 Unemployment: Excess =shortfall - hidden -0.09 0.03 - 0.92 -0.03 1.28 1.87 0.45 -0.35 Excess Shortfall 1.13 1.63 0.52 1.91 3.65 4.21 2.08 0.58 1.22 1.60 1.44 1.94 2.37 2.34 1.62 0.93 Hidden Employment: Shortfall and componen ts Shortfall 1.13 1.63 0.52 1.9 1 3.65 4.21 2.08 0.58 Wage 0.03 - 0.02 0.28 0.21 0.23 0.35 0.47 0.47 Demand 1.10 1.65 0.24 1.70 3.42 3.85 1.61 0.11 Unemployment: Excess and components -0.09 0.03 -0.92 -0.03 1.28 1.87 0.45 -0.35 Excess 0.25 0.21 0.42 0.39 0.34 0.46 0.61 0.71 Wage Demand -0.34 -0.18 -1.34 -0.42 0.94 1.41 -0.15 -1.06

1980

1981

1982

-0.41 5.85 6.26

0.99 7.29 6.31

2.25 4.52 8.57 10.76 6.32 6.24

-0.41 0.03 0.43

0.99 1.70 0.71

2.25 3.23 0.98

4.52 6.78 2.26

0.03 0.47 -0.45

1.70 0.61 1.10

3.23 0.46 2.77

6.78 0.85 5.93

-0.41 0.78 -1.19

0.99 0.85 0.13

2.25 0.72 1.53

4.52 0.89 3.63

component are quite similar to tho se in table 2, except during 1974-1976. Further insight into these results is provided by table 4. The top panel displays the actual, expected, and full-employment values for real wage rates used in the simulations. The difference between the actual and expected wages, and the associated wage gaps used in table 2, WRE- WRF, and table 3, W R - W RF, are shown in the second panel. The calculated employment shortfalls, EF - E, for the actu al and expected wage gap alternatives are in panel 3, and the corresponding estim ates of the wage component of excess unemployment are in panel 4.

1556

B.G. Hickman, Real wages, aggregate demand, and unemployment

Table 4 Wage surprises and employment effects. 1959

1963

1964

1965

1966

1967

1968

1969

1970

Actual. expected. and full-employment wage (dollars) 3.77 WR 3.29 3.39 3.53 3.68 3.46 3.24 3.35 3.58 3.76 WRE 3.74 WRF 3.32 3.42 3.50 3.62

3.92 3.84 3.87

4.06 4.01 3.98

4.26 4.21 4.02

4.34 4.42 4.15

4.51 4.48 4.28

4.64 4.70 4.35

4.70 4.82 4.39

Wage gaps (percent) 2.08 WR-WRE 1.46 1.15 2.89 WR-WRF 0.84 -1.04 -0.99 1.59 WRE-WRF -2.47 -2.12 -1.21 -1.26

0.24 2.10 0.90 1.25 0.65 -0.83

1.24 2.02 0.76

1.18 -1.95 4.55 5.89 4.66 6.63

Employment: Shortfall comparisons 1.42 2.30 ACT gap 1.86 EXP gap 1.34 2.17 1.81

1.82 1.89

0.53 -0.91 -0.60 -0.88 -0.64 0.50 -0.96 -0.42 -1.00 -0.51

0.31 0.49

1960

1961

1962

2.05 1.88

Unemployment: Wage component comparisons 0.08 0.10 ACT gap -0.01 0.00 EXP gap -0.06 -0.03 -0.01 -0.03 1971

1972

1973

1974

1.55 1.39

0.77 -1.27 -2.50 6.74 5.51 7.10 4.70 8.11 9.84

0.05 0.07 0.10 -0.05

0.11 0.08

0.30 0.25

0.20 0.35

0.28 0.18

0.35 0.45

0.35 0.49

1975

1976

1977

1978

1979

1980

1981

1982

4.98 4.94 4.48

5.05 5.05 4.51

5.12 5.14 4.53

5.16 5.18 4.64

5.32 5.13 4.68

0.80 -0.09 -0.31 -0.53 11.18 11.93 12.93 11.21 10.29 12.03 13.28 11.80

3.71 13.76 9.69

Actual. expected, and full IVR 4.74 IVRF 4.83 IVRF 4.52

employment wage (dollars) 4.83 5.03 4.93 4.68 4.82 4.96 5.23 5.07 4.67 4.73 4.64 4.41

4.81 4.59 4.47

4.91 4.81 4.47

Wage gaps (percent) WRF-WRE -1.95 4.89 WR-WRF IVRE-IVRF 6.98

0.04 3.30 3.25

1.40 -5.63 -7.64 6.20 6.22 6.19 4.73 12.57 14.97

4.78 7.53 2.62

1.96 9.68 7.58

4.21 3.38

2.08 2.06

0.58 0.57

0.03 0.07

1.70 1.73

3.23 3.28

6.78 6.30

0.34 0.46 0.75 -0.10

0.61 0.59

0.71 0.70

0.78 0.81

0.85 0.88

0.72 0.75

0.89 0.57

Employment: Shortfall comparisons ACT gap 1.13 1.63 0.52 EXP gap 1.22 0.39 1.65

1.91 2.55

Unemployment: Wage component comparisons ACT gap 0.25 0.42 0.21 0.39 EXP gap 0.32 0.26 0.32 0.84

3.65 4.25

The first point to notice is that the expectational error, W R - W RE, is quite small in many years and seldom exceeds 2 percent. The principal exception occurs during 1974-1976, when the error is much larger. The unanticipated energy shock depressed the actual real wage far below the expected level in 1974-1975, and these low realizations in turn reduced the expected wage below the actual level in 1976. Classical excess unemployment was therefore exacerbated by the failure to foresee the depressing effects on the real wage of the supply shock in 1974-1975, and correspondingly mitigated by the over-correction of real wage expectations in 1976.

B.G. Hickman, Real wages, aggregate demand, and unemploymell/

1557

Apart from the unanticipated and sizeable impact of the first energy shock, however, the general conclusion from tables 3 and 4 is that expectational errors normally are unimportant determinants of the magnitude of classical unemployment. This is partly because the expectational errors are fairly small as a rule, but also because of the low wage-elasticity of labor demand in the model. 8.2. Carryover unemployment and tile net demand gap

To what extent do the estimates of Keynesian unemployment in table 2 embody the carryover effect? Table 5 replicates the breakdown between the wage and demand components from table 2 and adds the decomposition of the latter between the carryover and output terms. The carryover component of the employment shortfall is usually positive and often substantial.P When account is taken of hidden employment, Table 5 Wage and demand components of unemployment (millions of persons). 1959

1960

1961

Employment shortfall and components Shortfall 2.17 1.34 1.81 Wage -0.20 -0.15 -0.08 Demand 1.54 1.97 2.24 Output gap 0.71 1.76 1.50 Carryover 0.83 0.49 0.46 Excess unemployment and components Excess 1.21 1.26 1.35 Wage -0.06 -0.03 -0.01 Demand 1.27 1.29 1.37 Output gap 0.54 1.15 1.34 Carryover 0.73 0.14 0.03 1971

1972

1973

Employmentshortfall and components 1.22 1.65 0.39 0.13 0.00 0.15 1.10 0.24 1.65 0.14 -0.84 O.lJ Carryover 0.96 1.08 1.51 Excess unemployment and components Excess -0.02 0.07 -1.02 Wage 0.32 0.26 0.32 Demand -0.34 -0.18 -1.34 Output gap 0.10 0.10 -0.62 Carryover -0.44 -0.28 -0.72

Shortfall Wage Demand Output gap

1962

1963

1964

1.88 -0.12 2.00 0.97 1.04

1.89 0.06 1.84 0.91 0.92

1.39 -0.11 1.51 0.56 0.94

0.50 0.05 0.44 -0.35 0.80

-0.96 0.22 -1.18 -1.73 0.55

-0.42 0.25 -0.66 -1.34 0.68

-1.00 0.04 -1.04 -1.49 0.45

-0.51 0.32 -0.84 -1.30 0.46

0.49 0.39 0.10 -0.27 0.37

1.10 -0.03 1.13 0.73 0.39

0.82 0.10 0.72 0.70 0.02

0.42 -0.05 0.47 0.43 0.04

-0.45 0.08 -0.53 -0.28 -0.25

-1.57 0.25 -1.83 -1.46 -0.36

-1.14 0.35 -1.49 -1.09 -0.40

-1.51 0.18 -1.69 -1.22 -0.47

-1.36 0.45 -1.81 -1.07 -0.74

-0.67 0.49 -1.16 -0.21 -0.95

1965

1966

1967

1968

1969

1970

19H

1975

1976

1977

1978

1979

1980

1981

1982

2.55 0.84 1.70 0.60 1.10

4.25 0.83 3.42 2.02 1.4()

3.38 -0.47 3.85 1.21 2.65

2.06 0.45 1.61 -0.28 1.89

0.57 0.46 0.11 -1.53 1.64

0.07 0.52 -0.45 -1.51 1.06

1.73 0.64 1.10 -0.07 1.17

3.28 0.51 2.77 0.89 1.88

6.30 0.37 5.93 3.55 2.38

0.42 0.84 -0.42 0.44 -0.86

1.69 0.75 0.94 1.42 -0.48

1.30 -0.10 1.41 0.83 0.57

0.44 0.59 -0.15 -0.20 0.05

-0.35 0.70 -1.06 -1.11 0.06

-0.37 0.81 -1.19 -1.11 -0.08

1.01 0.88 0.13 -0.05 0.18

2.29 0.75 1.53 0.63 0.91

4.20 0.57 3.63 2.47 1.16

IJNotice that the carryover component remains positive even in such high demand years as 1966-1969 arid 1978-1979. This is because the demand function for labor is in terms of manhours instead of unemployment. When expressed in manhours, the carryover component becomes negative under high demand conditions, but after correcting for the carryover component of average working hours, the employment shortfall stays positive.

EE.R.- C

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B.G. Hickman, Real wages, aggregate demand, and unemployment

however, it is found that the carryover component of excess unemployment is generally small and is negative more often than not. The output component measures the contribution of the current gap between actual and potential output to Keynesian unemployment. It was the dominant element in Keynesian unemployment during the 1960s, but the carryover effect assumed greater importance in 1970-1972, 1974, and 1981. It was argued above that the concept of Keynesian unemployment should include the carryover component. Insofar as the relative importance of classical unemployment is concerned, however, it is little affected by the choice between the total demand and the output components as the basis for comparison. It is true on either basis' that classical unemployment was dominant in 1974, 1977 and 1980, that high effective demand overwhelmed the effects of high real wages in 1978-1979, and that deficient demand was the major depressant in 1975-1976 and 1982. Thus, of the earlier characterizations based on the preferred demand measure, only the observation that deficient demand was primarily responsible for excess unemployment in 1981 would be altered if the output gap were instead adopted as the yardstick for Keynesian unemployment. 9. Conclusions The new approach to distinguishing classical and Keynesian unemployment presented in this paper is based on behavioral hypotheses at variance with the competitive paradigm underlying the traditional fixprice models. Since prices are set as a markup over normal unit labor cost, real wages are sticky and long-run equilibrium is achieved primarily through price level variation and the Keynes and Pigou effects. The demand for labor is conditional on output and its real wage elasticity is restricted to the substitution effect. Keynesian and classical unemployment may coexist instead of occupying separate regimes as in the rationing model with competitive product markets. The approach could be implemented in any econometric model with the foregoing characteristics. Some aspects of the current application are necessarily specific to the HC Model, of course. The carryover component of Keynesian unemployment, for example, would not be present in a model which did not measure potential output along a natural growth path. The numerical results on the real wage component would differ for aCES production function with a substitution elasticity departing from unity. A different hypothesis on the formation of wage and price expectations could also affect the measured responses. The quantitative importance of expectational errors and the carryover effects of past disequilibrium in the labor market were investigated, however, and were found to leave unaltered the conclusion that aggregate demand has

B.G. Hickman, Rea/wages, aggregate demand, and uncmp/oymcllt

1559

been the major determinant of cyclical unemployment in the U.S. economy except in isolated years. Given the restriction that labor demand is constrained by output, moreover, the elasticity of substitution would have to be substantially above unity, contrary to most econometric evidence which places it at or below unity, before the wage gap would provide the dominant explanation of excess unemployment.

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