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The anticipated real interest rate, capital utilization and the cyclical pattern of real wages
Journal of Monetary
Economics 13 (1984) 17-30. North-Holland
THE ANTICIPATED L INTEREST RATE, CAPITAL UTILIZATION AND THE CYCLICAL PAITERN OF REAL WAGES
This paper develop% a channel thrnu which increases in anticipated real intere>.t rate> can be ‘expansiortary’ for current bgyegate labor demand and current output ~ppll; The key feature of the model is the introductio: of a user cost of capital utdization which confronts the firm with the intertemporal problem of the optimal choices of capital utilization and depreciation. The resultmg variation in capital utilizatloa and capital services i.1 respons to tluctuations In rbe real rate of interest shifts the marginal product of labor and. thus. the demand for labor at the >,arne time and in the same direction that Lucas-Rapping real interest rate effects operate on labs-r suppl>. The complete model places no cl prrorr restrictions on the cyclical pattern of real wages. thus avoiding the countercyclical redI wage prediction made by Keynes and variou. 4 classical Mters that I> rejected by the data. Estimates crf a labor demand schedule for the annual U.S data reveal a significantly positive real intercsl rate effect.
I. introduction
An apparent problem in the current state of labor market theop is the ate real wages to display the significant negati\x observed failure of a employment predicted by both neoclassical and correlation with aggt Keynesian theories of employment determination. The key element underlvinp this common prediction of both theories is their shared view that firms operate along a @ueCrlabor demand schedule that. for a given stock of capital. is downward slop in the real wage-employment plane due to the standard assumption of returns to labor. Explanations of the ‘business cycle’ un m involve movements along hs labor demand schedule. not shifts in the schedule itself.’
1IR
J. J. Murick,
Jr., The unticipated red intcrvsr rute
The empirical question of whether the observed behavior of employment and real wages is consistent with this predictr:d negative correlation has been the subject of frequent investigation over the forty years since the original Dunlop (193$) and Tarshis (1939) procyclical real wage evidena:. Studies by Kuh (1966:) and Bodkin (1969) show that simple contemporaneous regression amalysis provides no evidence of any significant relationship :betwee wages emd employment. Neftci (1978) suggests that the failure of earlier studies to discern a significant inverse real wage-employment relation is a result of their exclusion of the possibility that this relationship may b,e distributed through time. * Alternatively, Tatom (1980) reports a significant contemporaneous negative employment-real wage corr&ion for the annual data once the effect of procyclical variation in capacity utilization rates on productivity is removed. Tatom”s findings suggest that firms face an interesting optimal capital utilization decision which is deterntined jointly with the labor demand decision. However, he provides no theory as to why firms should choose to vary their utilization rates in a procychcal manner. The aims of this paper ;Ire to exphcitly develop the joint capital utilization-labor demand problem within a model which focuses on the intertemporal substitution of capital services on the part of firms and to test the moclel’s implied explanation of how the failure of real wages to be negatiively correlated with employment can be reconciled with a neoclassical produc:tion function subject to diminishing marginal factor returns. 2. Behavior of the firm The representative firm’s problem is studied here within a two-period setting. As regards the firm’s stock of capital, we will assume that units of physical capital become completely specialized to the individual firm once in place so that no market exists for the firm’s existing stock of capital. Further, WC assume &at there is no possibility for the creation of new capital goods 50 thar the firm has no investment demand problem and regards its inherited capita stock as a depreciable, non-renewable resource. The firm is assumed to face a production function of the form
Y = F( u, K, L),
FL,u,FKKrF;.,. < 0,
(1:
where 1’ is defined to be the flow of real output of the final product, K is the ‘Sargent(1978) develops a dynamic labor demand schedule based upon rapil;i courts “)I labor force adplstment wJhichis consktant with Neftci’s evidence. Howcvcr. Geap and Kenna~ (IX?) question the robustness of Nefici’s findings.
existing stock of capital, C’ is an index of the rate of capital utilization (0 5 iJ : 1) measured in hours of capital usage per period and L is the flow of . Within this formulation, output depends upon capital s employed with the former depending upon Lfand K wily equal to the product t[K. In addition to the standard tgmal product of each input is both positive and t to increws in its own usage, the production LLinrtion assumes that utihzation and capital are each complementary to I-roar in production. Further, we assume that the firm is faced with a ‘user cost’ of capital utilization. Specifically, we posit that while an increase in the capital utilization rate raises both output and the marginal product of labor, it has an adverse effect on the rate of the physical depreciation of the existing capital stock. It is assumed that the relationship between the depreciation rate. S. and the capital utilization rate, L’, takes the form S = S(U),
S’>O,
S”SO.
(2)
This concept of a user cost of capital was discussed by Keynes 41936) and formalized by Taubman and Wilkinson (1970). The firm seeks to maximize its present value (equal to the present value of
the net cash flows due from the operation of its capital stock) PC/-PF(L,K,L)-WL+
CR)(Pf-(i’. It:. i, -
- tii}.
(3)
subject to the depreciation function describing the time path of its capital :\tock (using carets here and above to distinguish planned future values from current values of each variable) ii-
[l -S(U)]
K.
(4)
Taking P, its current product price, MI, the current wage rate, R. the current nominal interest rate, p, the currently expcctecl future product price. Ci-.the currently expected future w8 e rate and K. the current capital stock. as given. the firm chooses U. 0, L, and i to maximize (3) subject to (4). The tit-m’s first-order eficiencv conditions are
J. J. bIerrick,
20
Jr., The anticipated
real interest rute
Condition (5a) states that the firm chooses th’eoptimal current rate of capital utilization such that the marginal current return from utilization is just offset by the discounted marginal future return foregone due to the additional physical depreciation of the capital stock caused by additional current utilization. A slight rearrangement of (5a) shows ghat the optimal capital utilization decision can be interpreted as the marginal equality of the real cost of utilization and the atnticipjated real product rate of return (real interest rate)
Pa’) Condition (5b) implies that the firms should always choose 0, the terminal period’s utilization rate, to eq\ual unity since there is no return to saving capital from fuli depreciation. Conditions (5~) and (5d) are the standard marginal productivity-real factor cost equalities for labor in each period. Simultaneous solution of the four efficiency conditions (5a)-(5d) yields derived input demand functions of the following form:
Od=l,
(W 0% P(l+R) li
,+Ld i
(64
-
where the sign beneath each argument is the sign of the partial derivative of the particular function with respect to the particular argument under the assumption that the second-order conditions hold.” It is of primary interest t.o examine the effect of a rise in the anticipated real interest rate on the firm’s input choices. Ceteris paribus, a rise in the anticipated real interest rate will induce the firm to increase the current rate of capital utilization, increase the amount ‘Robert King (1980) has independently derived a similar labor demand function from an assumption that future production possibilities are negatively related to the amount of currently employed labor services.
J. J. Merrrch. Jr.. The untrc-rpuled real mtere.st row
11
of labor services employed and decrease the planned amount of labor to be employed in the future. The increase in current utilization results because the rise in the real interest rate induces the firm to incur the increased capital depreciation costs associated with the higher utilization since it implies that curnnt output has risen in value relative to future output. Since utilization and capital are assumed to be complementary factors to labor production. the new er rate of current utilization both raises the marginal product of current Babcr and simultaneously lowers that of future labor since increased current uuhzation implies less capital available for workers in the future period. The key positive effect of the anticipated real interest rate on current labor demand thus depends crucially upon two factors: (1) the engineering relationship between utilization and capital depreciation, and (2) the complementarity of utilization and labor in production. The effects of changes in the current real wage or the expected future real wage on input choices operate in similar fashion. Finally, these input demand functions along with the production function (1) imply that the current commodity supply function of the representative firm has the following form:
w * i +p ‘P’-$-‘+, -
P(l+R)
ys_ys
.
i
K
(7)
This commodity supply function along with the input demand functions describe the behavior of the firms in the complete macroeconomic mLJdelof section 3.
3. The complete model
In this section we impose the input demand and commodity supply functions, developed in section 2, on a ‘real’ business cycle model which explicitI> distinguishes between labor arld commodity markets withiD a general market framework. Our outline of the complete model describes the labor and commodity markets along with a discussion 19f the rote of the government.
regate demand schedule for labor Ey. (8‘, presents a stochastic loglinear of the representative firm’s labor services. It is based on a loglinear versi e tower-case b les are the r,atur;il logarithms of ~~ernandSC the corresponding variables defined in section 2 except for r. the expected real
22
J. J. Merrick, Jr., The anncipated real interest rutr
rate of interest, which is defined as R - b + p = ln( P(l + R)/P),4 fd=f~+I,dr-i~,~(w-p)+f~,B()i)-j))+l~k+~~.
(8)
The total supply of current employee hours is assumed to take the form of the labor supply function derived by Lucas and Rapping (1970). I” = 1; + I,“r+ lt,,p (w--P)-r~~~(~-p)-f;:a-t&*.
(9)
Here, the variable a represents the logarithm of the stock of real non-human wealth held by househo1d.s at the beginning of the initial period. The posited signs on the partial derivatives in (9) - and i.7 the commodity demand function below - embody the key Lucas-Rapping assumptions that consumption in both periods and future leisure are substitutes for current leisure and that the substitution effect of any price change outweighs the corresponding ‘wealth’ ef%ct. 3.2. The commodity market Aggregate commodity supply (10) is assumed to be given by a stochastic Soglinear version of the representativ. firm’s supply function (7). y” = _v;+ y,“r - J$,~ (w -p)
+y;,,-( ti -p)
+J$k + PJ.
WI
Aggregate commodity demand (11) is the Lucas-Rapping household commodity demand function augmented by a government shift variable, g, which captures the effect of transitory war-related real government purchases, yd=ygd-?:dr+y~,,pQW’--)+y~,P(~-B)+yuda+_,dg+Eq.
(111
The model is closed un’der the equilibrium conditions that l= Id = 1” and y = yd = y”. Taking the beginning of period levels of the capital stock and real non-human wealth as predetermined, the model’s five real variables - y, I, u, Y, and w -p - can be solved for explicitly in terms of the expected future real wage, the current value of the government purchases variablle, the capita! stock, real wealth and the stochastic terms from consideration of the commodity and labor market clearing conditions. 3.3. Role of the goverzmenr
In the model above the government affects the economy through its warreiated purchases in the clommodity market. As stressed by Hall (1980), the logic behin’d the use of a measure of war-related government commodity ‘For notational convenience, the real interest rate coefficients in the labor and commodity market schedules are referred to as the real interest rate elasticities. Actually, the coefficients rare &sticisics with respect to 1 + r.
demand fluctuations as the key impulse in an intertemporal business Chile model rests on the transitory nature of wars. Barro’r.(1981) empirical investigation of the impact of government purchases on real output indicates that the st ex~a~s~ona~ impact of government spending arises from temp~Xiry movements in real defense spending associated with wars, thus supporting Hall’s hypothesis. 4. Solution of the modd General market clearing requires values for the real interest rate and the reai wage that sirnult~ne~u~l~ clear tcrth the commodity and labor markets. The solution for these equilibrium vah~es yields ‘reduced-form’ expressions fcr the model which can be written in matrix form as
M = lIfX + E, w-p r
Al==
i
?’ U
where
I .
(12) &I &. -
x==
B
k
a
1
II is a conformable (5 x 5) matrix of reduced-form coetficients. and E‘ is a (5 x 1) vector of disturbance terms. We now focus on fluctuations in transitory war-related real gmxrnment purchases as a key source of business cycle fluctuations arLdthe implications of the present model for the sign of the reai wage-employment correlation. The effects of a change in trnneitary real government purchases on real wages and employ ment are iven, respectively, by q, and r3, in (12) where. letting ilnd~~,,,=j&,-q: /,. L-y -1: “ ,,+I~,,,.!;==~:“+?;d ,/
ensures that hot
the numerator and denominator of yII are positive w that
24
J. J. Merric-k., Jr., The anticipated rear!imrest
rate
Table 1 StructurJ versus reduced-form restrictions. Structural eiasticities
Reduced-form relation
Cyclical pattern in real wages
(1)
Countercyclicill
(2)
Noncyclical
(3)
Procyclical
employment varies directly in response to fluctuations in g. Given that njtJ> 0, the sign of the covariance between real wages and employment is dependent upon the sign of mii whichi,in turn depends upon the relative magnitudes of if and I;, the elasticities of I.abor deru?nd ant4 labor supply with respect to the real w,age. Table 1 smnmarizes the model’s restrictions regarding the relative magnitudes of the structural real interest rate elasticities, the reduced-form real wage-government purchases coefficient and the sign of the cyclical pattern in real interest rate.” If 1;: < I;, t1ie ultimate increase in the anticipated real interest rate necessary to. cle’ar the commodity market given the initial shock to commodity demand via a rise in g creates excess suppb~ in the labor market which can only be eliminated by a fall in the real wage as employment and output expand. Thus, real wages will follow a countercyclical pattern. This case is relevant in the standard static labor demand function without endogenous variation of the capiial utilization rate by firms (If = 0). If,, instead, 1: = Is, the model predicts that no cyclic4 pactern in real wages will be observed. Finally, in the case in which I,”> l,S,real wages will beprocydicul since the rise in the anticipated real interest rate necessitated by the expansionary government expenditure shock will cause excess labor demand which will lead ultimately to higher real wages. 5,. Empirical iresults In this section we estimate and test the business cycle model developed above using annual data over the 1950-1978 sample period. The emphasis is placed upon estimating the parameters of the labor market subsector and testing the signific~anceof the structural labor demand versus labor supply real interest rate elasticities as relevant for the determination of the cyclical pattern of real wages. The estimates of the structural parameters are obtained throu a mod&M two-stage-least-squares procedure motivated by our use of the ex JJOSFreal interest rate as an empirical proxy for the directly unobservable ‘Our assumption that the sign of the real wage government purchases coefficient determines the sign of the realwagc-employm~J:ntcovariance implicity assumes that other sourc~:sof labor market schedule displacement @roduct.ivity shocks, etc.) are relatively unimportant.
anticipated real interest rate. By definition, the ex pm real rate equals the true anticipated real rate minus the public’:; realized inflation forecasting error. Mishkin’s (1980) results imply that the e.y post data can be used to unbiasedlp estimate the coefficiefits of the ‘first-stage’ regression for the anticipated real interest rate withes a two-stage-least-squares procedure for estimating the labor demand and sup y -schedules.However. the inflation forecast error ‘noise’ in the PX post real te data will lead to an overstatement of the true standard errors of the real rate e cients in both of the estimated labor market schedules under the standar wo-stage-least-squares algorithm.” To offset this upward bias in the ‘second-stage’ regressrons’estimated standard errors due to the inflation error noise, the estimat standard errors reported below are calculated wathcmt the substitution o e ex pm-t real rate for its first-stage projection in the second-sta iabor market regressions.’ This procedure implicitly attributes the .sourceof all the residual variance in thtz CJ.\: PO.U 1-ea1rats ssion to unexpected inflation.” assumption that the eqdihrium real ~aagr:process g-mot be distinguished from that of a ‘random Nalk with drift’ signiflcantl>, simplifis5 our analysis of the anticipated future red1 wage, which appears as a determinant of both the demand and supply of labor. Altonji and Ashenfeller ( 1980) ence supporting this statistical specification for the annual have provided e nder this specification for the equilibrium real wage prb’cess. real wage data.’ the expected future real wage can be suppressed in the empirical anal?:& hince the current real wage itself appears ir. both labor market 3chedules. T3e estimated labor market elasticities will b;t unbiased except for the current real wage elasticities. The estimated labor lienland elastictty Cl1 actuali>, equal --(I:.~, - I$,,,), while the estimated labor supply elasticit! will actuali>, ~+,a1 ( 1: ;I ,’ - I$‘$
).“’
26
J. J. Met-rick, Jr., The anricputed
real irlrerest
rute
As our measure of labor services, we use the annual value of aggregate private non-farm employee-hours in the U.S. economy. The ex post real rate variable is the annual average of nominal interest rates WI three-month Treasury bills minus the one-year-ahead continuously compounded rate of inflation as measured by the change in the logarithm of the annual gross national product deflator. l1 The current seal wage is measured as private non-farm average hourly compensation deflated by the gross national product ,deffator. while the beginning of period stock of real non-human wealth is crudely measured as the prior year’s value of the Standard and Poor’s 500 Stock Index deflated by the,lagged value of the GNP deflator. Finally. the transitory war-related government purchases variable is measured as Barro’s construct of the deviation of the ratio of rea defense purchases to real GNP from its ‘normal’ value. Estimates of the labor market parameters
Table 2, rows (1) and (2) reports the results of the two-stage-least-squares estimation of the labor demand and supply functions, respectively. All variables except the real interest rate and the transitory defense purchases measures appear in logarithmic form. Note that the labor demand function includes the relative price of energy measured as the logarithm of the processed fuels and lubricants component of the producer price index deflated by the GNP deflator. The relative price of energy is included to account for the possibility of labor demand effects due to economization by firms on energg inputs resulting from the dramatic rise in energy prices after 1973.” The sign of the labor demand elasticity with respect; to the relative price of energy (treated as exogenous) depends on whether labor and energy are complements or substitutes in production. Further, a time trend is added to each equation to capture any deterministic forces left unaccounted for by the model.” The ‘first-stage’ regressions use transitory defense purchases, real wealth and the relative price of processed fuels and lubricants along with a time trend as the exogenous and predetermined variables.
“This annualized average of the three-month bill rates is used in the aksrn~c of onr-yc;tr bill:rates over the earher part of the sample period. “See King and Tatom and their references for additional discussion and cviclencc. 131n the labor demand function, the time trend accounts for both technological change and baseline growth in the net capital stock. The Bureau of JSconomicAnalysis’s measure of the net non-farm private capital stock was included as an additional explanatory variable but was tnsignjticant. One might expect trouble with this capital stock measure since the BEA consteucts its series under the assumption that annual depreciation is a constant percentage of the existing stock whereas our model views depreciation as varying directly with the firm’s choice of capital usage. u5, the BEA’s net capital stock measure is biased in that it understates (overstates) the true depreciation of thy capital stock during years of high (low) utilization. creasur)
77
Estlmaciesof the lahix market schedules ard rca wage rcdwcd-form:
1950- 1978.”
h@ne-tai! significance at the 0.05 test level. ’ Two-M significance at 0.05 test level. JNot significantly dilfercnt from zero at 0.05 tt’s*tlcvcl
The estimated labor demand function reported in row (1) corresponds closely to that predicted by the model of firm behavior developed in :iection 2. Movements in the real interest rate have significantly positive effects on the quantity of labor demanded. while the impact of the real \vage has the atike effect. Labor demand is negatively related to the relati\xz y suggesting that labor and energy are uomplementsr> input>. The point estimate of 2.86 for the elasticity of laf80r demand with respect to the real interest (significantly positive at the five percent lei,el) reveals tha[ firms increase ct:rrent labor demanded in response to anticipated intertemporal shifts in final product demand. The lower and upper limits of the ninety-ti1.c: percent confidence interval of our estimate of this key parameter are 0.12 ancl 5.60, respectively. The paint estimate of the elasticity of labor demand with nificantly negative at the five pcrwnt respect to the real wa level. The ninety~~ve interval for our estimate of tht: I&,-,demand real wage elasGcitl)- lies between the boundc#of -- 0.77 imd - 6.93.‘” The &mated ‘labor supply function for the private non-f;lrnl WI~V I’xted in row (2, of tnkle 2. Uoth the real interest rate and the real v;;lgt’ hale e, though imprecisely measured. cfkcts on labor hup I!. The imprlxkon of
28
J. J. Merri&
Jr., The uttrrcipurcd red irrtcrtw rute
these labor supply estimates is reflected in the facts that the ninety-five percent interval for the real interest rate elasticity lies between limits of - 0.68 and 12.22 while that of the real wage elasticity has bounds of - 1.81 and 11.63.r5 A minor, insignificantly negative real wealth effect is also present in the labor supply equation, Again, a time trend is included to capture the effects of any deterministic forces left unaccounted for by the model. Aside from the complete conformity of their estimated signs with those predicted by the theory, the most striking aspect of the labor market parameter point estimates reported here is the magnitude of the measured real interest rate elasticities for both labor demand and supply. Point estimates of 2.86 and 5.77, respectively, for the labor demand and supply elasticities with respect to the anticipated real interest rate might : Gemimplausibly high and may suggest that the model is m&specified.l6 Oln the other hand, an explanation of observed fiuctuations in employment and real output in terms of an intertemporal substitution model requires lablor market schedules that imply elastic responses to real interest rate changes. The highly elastic schedules estimated here seem to provide some support for the recent interest in using intertemporal channels to explain business cycle fluctuations. Finally, we turn to an analysis of the model’s prediction for the sign of the ‘cyclical’ pattern of real wages. Wow (3) of table 2 presents our estimate of the real wage reduced-form. Note that the relationship between the estimated reduced-form coefficient for the effect of transitory real government purchases on real wages (?rrr of section 5) and the estimated structural labor demand and supply elasticities with respect to the real interest rate reported in table 2 corresponds to the pattern predicted by the model as summarized in table 1. In particular, v;e find that a significantly positive labor demand effect exists, that the elasticities of labor demand and supply do not differ significantly in m;%gnitudefrom each other and that the coefficient for the transitory governmcnt purchases variable in the real wage reduced-form is not significantly different from zero. Thus, the evidence supports the model as providing a counterexample to Geary and Kennan’s conjecture that it is ‘unlikely that one could find omitted variables which influence both sides of the market in the manner necessary to produce the observed empirical results’ of statistical irkdependence of the real wage and employment time series.
confidence
I on with which the labor supply real intcrsst rate clusticify is cst:matcd ih 15The imprec’si disappointing though not completely unexpected in view of previous evidence. See 1 wa aud Rapping and also Hall.
‘(‘Data for 1948 and 1949 were originally included but subsequently dropped from the sample as they produced large errors in the real wage ‘first-stage’ and generated mllated (and insignificant) labor demand real interest rate and real wai;e elasticity estimates of 12.X and - 11.4, respectively. Mowever. the chosen 1950-1978 period does encompass the Korean and Vietnam war years in order to ensure sufficient variation in the transitory government defense expenditures variable. the model’s featured exogenous force.
9. J. Merrd
Jr..
The antrc-rpared red meresr rue
29
6. Chchding mm The analysis of ehe firm’s intertemporal maximization probiem presented
here
was
undertaken with the initial capital stock viewed as depreciable but fo that no sibihty existed for purchases of addition,aI units of newly-produced capi investment). The major problem posed by the introduction of a market for newly-pr~uc~ capital goods is that, within a perfect-market. complete info~nla~ion neoclassical model. investment demand is unambiguously negatir~ly related lo the anticipated real interest rate. Since our model implies that real interest rates vary procyclically, real investment must be cmmercyciicai - a prediction that is easily refuted by the data. Models capable of ~x~~aini~~/U&Ythe procyclical pattern in investment and procyclical capital utilizatnon may require a ‘time-to-build’ technology for capital accumulation as suggested by Barro and King (1982) or financial market imperfections reyulring firms to internally finance some part of their desired investment expenditures. Finally, it is important to emphasize that the ‘expansionary’ real interest rate effect on labor demand reported here within the capital utilization-depreciaGon framework is significant n3t only in regard to the cyclical pattern of real wages issue but also in providing an alternative to reliance on labor supply real interest rate effects as the transmission mechanism for intertemporal shocks. This point is of particular importance both because it lowers the magnitude of the labor supply real interest rate elasticity necessary to explain ohsened business cycle fluctuations and because of the generally poor results of attempts to empirically do‘;ument significant real interest rate effects on labor nonrtmewabie
supply.‘9
JMorE
B
30
J. J. Merrick, Jr,, The anticipated real interesl rule
Kuh, E., :1975, Employment, production functions and effective demand, Journal of Political Economy. *Dec. Lucas, R.E. and L. Rapping, 1970. Real wages, employment and inflation, in: Edmund Phclps, cd., Microeconomic foundations of employment and inflation theory (Norton, New York). Mishkin, !F.. 1980, The real interest rate: An empirical investigation, Paper presented at the Carnegie-Rochester Conference, Nov. Neftci, S., 1978, A time series analysis of the real wages-employment relationship, Journal of Political Economy, April. Sargent, I’., 1978, Estimation of #dynamiclabor demand schedules under rational expectations, Journal $I Political Economy, Dec. Tarshis. L., 1939, Changes in real and money wges, Economic Journal, March. Tatom, J., 1980, The problem of procyclical real wages and productivity, Journal of Political Economy. Taubman. P. and M. Wilkinson, 1970, User cost, output and unexpected price changes, in: Edmund Phelps, ed., Microeconomic foundations of employment and inflation theory (Norton, New York).
Economics 13 (1984) 17-30. North-Holland
THE ANTICIPATED L INTEREST RATE, CAPITAL UTILIZATION AND THE CYCLICAL PAITERN OF REAL WAGES
This paper develop% a channel thrnu which increases in anticipated real intere>.t rate> can be ‘expansiortary’ for current bgyegate labor demand and current output ~ppll; The key feature of the model is the introductio: of a user cost of capital utdization which confronts the firm with the intertemporal problem of the optimal choices of capital utilization and depreciation. The resultmg variation in capital utilizatloa and capital services i.1 respons to tluctuations In rbe real rate of interest shifts the marginal product of labor and. thus. the demand for labor at the >,arne time and in the same direction that Lucas-Rapping real interest rate effects operate on labs-r suppl>. The complete model places no cl prrorr restrictions on the cyclical pattern of real wages. thus avoiding the countercyclical redI wage prediction made by Keynes and variou. 4 classical Mters that I> rejected by the data. Estimates crf a labor demand schedule for the annual U.S data reveal a significantly positive real intercsl rate effect.
I. introduction
An apparent problem in the current state of labor market theop is the ate real wages to display the significant negati\x observed failure of a employment predicted by both neoclassical and correlation with aggt Keynesian theories of employment determination. The key element underlvinp this common prediction of both theories is their shared view that firms operate along a @ueCrlabor demand schedule that. for a given stock of capital. is downward slop in the real wage-employment plane due to the standard assumption of returns to labor. Explanations of the ‘business cycle’ un m involve movements along hs labor demand schedule. not shifts in the schedule itself.’
1IR
J. J. Murick,
Jr., The unticipated red intcrvsr rute
The empirical question of whether the observed behavior of employment and real wages is consistent with this predictr:d negative correlation has been the subject of frequent investigation over the forty years since the original Dunlop (193$) and Tarshis (1939) procyclical real wage evidena:. Studies by Kuh (1966:) and Bodkin (1969) show that simple contemporaneous regression amalysis provides no evidence of any significant relationship :betwee wages emd employment. Neftci (1978) suggests that the failure of earlier studies to discern a significant inverse real wage-employment relation is a result of their exclusion of the possibility that this relationship may b,e distributed through time. * Alternatively, Tatom (1980) reports a significant contemporaneous negative employment-real wage corr&ion for the annual data once the effect of procyclical variation in capacity utilization rates on productivity is removed. Tatom”s findings suggest that firms face an interesting optimal capital utilization decision which is deterntined jointly with the labor demand decision. However, he provides no theory as to why firms should choose to vary their utilization rates in a procychcal manner. The aims of this paper ;Ire to exphcitly develop the joint capital utilization-labor demand problem within a model which focuses on the intertemporal substitution of capital services on the part of firms and to test the moclel’s implied explanation of how the failure of real wages to be negatiively correlated with employment can be reconciled with a neoclassical produc:tion function subject to diminishing marginal factor returns. 2. Behavior of the firm The representative firm’s problem is studied here within a two-period setting. As regards the firm’s stock of capital, we will assume that units of physical capital become completely specialized to the individual firm once in place so that no market exists for the firm’s existing stock of capital. Further, WC assume &at there is no possibility for the creation of new capital goods 50 thar the firm has no investment demand problem and regards its inherited capita stock as a depreciable, non-renewable resource. The firm is assumed to face a production function of the form
Y = F( u, K, L),
FL,u,FKKrF;.,. < 0,
(1:
where 1’ is defined to be the flow of real output of the final product, K is the ‘Sargent(1978) develops a dynamic labor demand schedule based upon rapil;i courts “)I labor force adplstment wJhichis consktant with Neftci’s evidence. Howcvcr. Geap and Kenna~ (IX?) question the robustness of Nefici’s findings.
existing stock of capital, C’ is an index of the rate of capital utilization (0 5 iJ : 1) measured in hours of capital usage per period and L is the flow of . Within this formulation, output depends upon capital s employed with the former depending upon Lfand K wily equal to the product t[K. In addition to the standard tgmal product of each input is both positive and t to increws in its own usage, the production LLinrtion assumes that utihzation and capital are each complementary to I-roar in production. Further, we assume that the firm is faced with a ‘user cost’ of capital utilization. Specifically, we posit that while an increase in the capital utilization rate raises both output and the marginal product of labor, it has an adverse effect on the rate of the physical depreciation of the existing capital stock. It is assumed that the relationship between the depreciation rate. S. and the capital utilization rate, L’, takes the form S = S(U),
S’>O,
S”SO.
(2)
This concept of a user cost of capital was discussed by Keynes 41936) and formalized by Taubman and Wilkinson (1970). The firm seeks to maximize its present value (equal to the present value of
the net cash flows due from the operation of its capital stock) PC/-PF(L,K,L)-WL+
CR)(Pf-(i’. It:. i, -
- tii}.
(3)
subject to the depreciation function describing the time path of its capital :\tock (using carets here and above to distinguish planned future values from current values of each variable) ii-
[l -S(U)]
K.
(4)
Taking P, its current product price, MI, the current wage rate, R. the current nominal interest rate, p, the currently expcctecl future product price. Ci-.the currently expected future w8 e rate and K. the current capital stock. as given. the firm chooses U. 0, L, and i to maximize (3) subject to (4). The tit-m’s first-order eficiencv conditions are
J. J. bIerrick,
20
Jr., The anticipated
real interest rute
Condition (5a) states that the firm chooses th’eoptimal current rate of capital utilization such that the marginal current return from utilization is just offset by the discounted marginal future return foregone due to the additional physical depreciation of the capital stock caused by additional current utilization. A slight rearrangement of (5a) shows ghat the optimal capital utilization decision can be interpreted as the marginal equality of the real cost of utilization and the atnticipjated real product rate of return (real interest rate)
Pa’) Condition (5b) implies that the firms should always choose 0, the terminal period’s utilization rate, to eq\ual unity since there is no return to saving capital from fuli depreciation. Conditions (5~) and (5d) are the standard marginal productivity-real factor cost equalities for labor in each period. Simultaneous solution of the four efficiency conditions (5a)-(5d) yields derived input demand functions of the following form:
Od=l,
(W 0% P(l+R) li
,+Ld i
(64
-
where the sign beneath each argument is the sign of the partial derivative of the particular function with respect to the particular argument under the assumption that the second-order conditions hold.” It is of primary interest t.o examine the effect of a rise in the anticipated real interest rate on the firm’s input choices. Ceteris paribus, a rise in the anticipated real interest rate will induce the firm to increase the current rate of capital utilization, increase the amount ‘Robert King (1980) has independently derived a similar labor demand function from an assumption that future production possibilities are negatively related to the amount of currently employed labor services.
J. J. Merrrch. Jr.. The untrc-rpuled real mtere.st row
11
of labor services employed and decrease the planned amount of labor to be employed in the future. The increase in current utilization results because the rise in the real interest rate induces the firm to incur the increased capital depreciation costs associated with the higher utilization since it implies that curnnt output has risen in value relative to future output. Since utilization and capital are assumed to be complementary factors to labor production. the new er rate of current utilization both raises the marginal product of current Babcr and simultaneously lowers that of future labor since increased current uuhzation implies less capital available for workers in the future period. The key positive effect of the anticipated real interest rate on current labor demand thus depends crucially upon two factors: (1) the engineering relationship between utilization and capital depreciation, and (2) the complementarity of utilization and labor in production. The effects of changes in the current real wage or the expected future real wage on input choices operate in similar fashion. Finally, these input demand functions along with the production function (1) imply that the current commodity supply function of the representative firm has the following form:
w * i +p ‘P’-$-‘+, -
P(l+R)
ys_ys
.
i
K
(7)
This commodity supply function along with the input demand functions describe the behavior of the firms in the complete macroeconomic mLJdelof section 3.
3. The complete model
In this section we impose the input demand and commodity supply functions, developed in section 2, on a ‘real’ business cycle model which explicitI> distinguishes between labor arld commodity markets withiD a general market framework. Our outline of the complete model describes the labor and commodity markets along with a discussion 19f the rote of the government.
regate demand schedule for labor Ey. (8‘, presents a stochastic loglinear of the representative firm’s labor services. It is based on a loglinear versi e tower-case b les are the r,atur;il logarithms of ~~ernandSC the corresponding variables defined in section 2 except for r. the expected real
22
J. J. Merrick, Jr., The anncipated real interest rutr
rate of interest, which is defined as R - b + p = ln( P(l + R)/P),4 fd=f~+I,dr-i~,~(w-p)+f~,B()i)-j))+l~k+~~.
(8)
The total supply of current employee hours is assumed to take the form of the labor supply function derived by Lucas and Rapping (1970). I” = 1; + I,“r+ lt,,p (w--P)-r~~~(~-p)-f;:a-t&*.
(9)
Here, the variable a represents the logarithm of the stock of real non-human wealth held by househo1d.s at the beginning of the initial period. The posited signs on the partial derivatives in (9) - and i.7 the commodity demand function below - embody the key Lucas-Rapping assumptions that consumption in both periods and future leisure are substitutes for current leisure and that the substitution effect of any price change outweighs the corresponding ‘wealth’ ef%ct. 3.2. The commodity market Aggregate commodity supply (10) is assumed to be given by a stochastic Soglinear version of the representativ. firm’s supply function (7). y” = _v;+ y,“r - J$,~ (w -p)
+y;,,-( ti -p)
+J$k + PJ.
WI
Aggregate commodity demand (11) is the Lucas-Rapping household commodity demand function augmented by a government shift variable, g, which captures the effect of transitory war-related real government purchases, yd=ygd-?:dr+y~,,pQW’--)+y~,P(~-B)+yuda+_,dg+Eq.
(111
The model is closed un’der the equilibrium conditions that l= Id = 1” and y = yd = y”. Taking the beginning of period levels of the capital stock and real non-human wealth as predetermined, the model’s five real variables - y, I, u, Y, and w -p - can be solved for explicitly in terms of the expected future real wage, the current value of the government purchases variablle, the capita! stock, real wealth and the stochastic terms from consideration of the commodity and labor market clearing conditions. 3.3. Role of the goverzmenr
In the model above the government affects the economy through its warreiated purchases in the clommodity market. As stressed by Hall (1980), the logic behin’d the use of a measure of war-related government commodity ‘For notational convenience, the real interest rate coefficients in the labor and commodity market schedules are referred to as the real interest rate elasticities. Actually, the coefficients rare &sticisics with respect to 1 + r.
demand fluctuations as the key impulse in an intertemporal business Chile model rests on the transitory nature of wars. Barro’r.(1981) empirical investigation of the impact of government purchases on real output indicates that the st ex~a~s~ona~ impact of government spending arises from temp~Xiry movements in real defense spending associated with wars, thus supporting Hall’s hypothesis. 4. Solution of the modd General market clearing requires values for the real interest rate and the reai wage that sirnult~ne~u~l~ clear tcrth the commodity and labor markets. The solution for these equilibrium vah~es yields ‘reduced-form’ expressions fcr the model which can be written in matrix form as
M = lIfX + E, w-p r
Al==
i
?’ U
where
I .
(12) &I &. -
x==
B
k
a
1
II is a conformable (5 x 5) matrix of reduced-form coetficients. and E‘ is a (5 x 1) vector of disturbance terms. We now focus on fluctuations in transitory war-related real gmxrnment purchases as a key source of business cycle fluctuations arLdthe implications of the present model for the sign of the reai wage-employment correlation. The effects of a change in trnneitary real government purchases on real wages and employ ment are iven, respectively, by q, and r3, in (12) where. letting ilnd~~,,,=j&,-q: /,. L-y -1: “ ,,+I~,,,.!;==~:“+?;d ,/
ensures that hot
the numerator and denominator of yII are positive w that
24
J. J. Merric-k., Jr., The anticipated rear!imrest
rate
Table 1 StructurJ versus reduced-form restrictions. Structural eiasticities
Reduced-form relation
Cyclical pattern in real wages
(1)
Countercyclicill
(2)
Noncyclical
(3)
Procyclical
employment varies directly in response to fluctuations in g. Given that njtJ> 0, the sign of the covariance between real wages and employment is dependent upon the sign of mii whichi,in turn depends upon the relative magnitudes of if and I;, the elasticities of I.abor deru?nd ant4 labor supply with respect to the real w,age. Table 1 smnmarizes the model’s restrictions regarding the relative magnitudes of the structural real interest rate elasticities, the reduced-form real wage-government purchases coefficient and the sign of the cyclical pattern in real interest rate.” If 1;: < I;, t1ie ultimate increase in the anticipated real interest rate necessary to. cle’ar the commodity market given the initial shock to commodity demand via a rise in g creates excess suppb~ in the labor market which can only be eliminated by a fall in the real wage as employment and output expand. Thus, real wages will follow a countercyclical pattern. This case is relevant in the standard static labor demand function without endogenous variation of the capiial utilization rate by firms (If = 0). If,, instead, 1: = Is, the model predicts that no cyclic4 pactern in real wages will be observed. Finally, in the case in which I,”> l,S,real wages will beprocydicul since the rise in the anticipated real interest rate necessitated by the expansionary government expenditure shock will cause excess labor demand which will lead ultimately to higher real wages. 5,. Empirical iresults In this section we estimate and test the business cycle model developed above using annual data over the 1950-1978 sample period. The emphasis is placed upon estimating the parameters of the labor market subsector and testing the signific~anceof the structural labor demand versus labor supply real interest rate elasticities as relevant for the determination of the cyclical pattern of real wages. The estimates of the structural parameters are obtained throu a mod&M two-stage-least-squares procedure motivated by our use of the ex JJOSFreal interest rate as an empirical proxy for the directly unobservable ‘Our assumption that the sign of the real wage government purchases coefficient determines the sign of the realwagc-employm~J:ntcovariance implicity assumes that other sourc~:sof labor market schedule displacement @roduct.ivity shocks, etc.) are relatively unimportant.
anticipated real interest rate. By definition, the ex pm real rate equals the true anticipated real rate minus the public’:; realized inflation forecasting error. Mishkin’s (1980) results imply that the e.y post data can be used to unbiasedlp estimate the coefficiefits of the ‘first-stage’ regression for the anticipated real interest rate withes a two-stage-least-squares procedure for estimating the labor demand and sup y -schedules.However. the inflation forecast error ‘noise’ in the PX post real te data will lead to an overstatement of the true standard errors of the real rate e cients in both of the estimated labor market schedules under the standar wo-stage-least-squares algorithm.” To offset this upward bias in the ‘second-stage’ regressrons’estimated standard errors due to the inflation error noise, the estimat standard errors reported below are calculated wathcmt the substitution o e ex pm-t real rate for its first-stage projection in the second-sta iabor market regressions.’ This procedure implicitly attributes the .sourceof all the residual variance in thtz CJ.\: PO.U 1-ea1rats ssion to unexpected inflation.” assumption that the eqdihrium real ~aagr:process g-mot be distinguished from that of a ‘random Nalk with drift’ signiflcantl>, simplifis5 our analysis of the anticipated future red1 wage, which appears as a determinant of both the demand and supply of labor. Altonji and Ashenfeller ( 1980) ence supporting this statistical specification for the annual have provided e nder this specification for the equilibrium real wage prb’cess. real wage data.’ the expected future real wage can be suppressed in the empirical anal?:& hince the current real wage itself appears ir. both labor market 3chedules. T3e estimated labor market elasticities will b;t unbiased except for the current real wage elasticities. The estimated labor lienland elastictty Cl1 actuali>, equal --(I:.~, - I$,,,), while the estimated labor supply elasticit! will actuali>, ~+,a1 ( 1: ;I ,’ - I$‘$
).“’
26
J. J. Met-rick, Jr., The anricputed
real irlrerest
rute
As our measure of labor services, we use the annual value of aggregate private non-farm employee-hours in the U.S. economy. The ex post real rate variable is the annual average of nominal interest rates WI three-month Treasury bills minus the one-year-ahead continuously compounded rate of inflation as measured by the change in the logarithm of the annual gross national product deflator. l1 The current seal wage is measured as private non-farm average hourly compensation deflated by the gross national product ,deffator. while the beginning of period stock of real non-human wealth is crudely measured as the prior year’s value of the Standard and Poor’s 500 Stock Index deflated by the,lagged value of the GNP deflator. Finally. the transitory war-related government purchases variable is measured as Barro’s construct of the deviation of the ratio of rea defense purchases to real GNP from its ‘normal’ value. Estimates of the labor market parameters
Table 2, rows (1) and (2) reports the results of the two-stage-least-squares estimation of the labor demand and supply functions, respectively. All variables except the real interest rate and the transitory defense purchases measures appear in logarithmic form. Note that the labor demand function includes the relative price of energy measured as the logarithm of the processed fuels and lubricants component of the producer price index deflated by the GNP deflator. The relative price of energy is included to account for the possibility of labor demand effects due to economization by firms on energg inputs resulting from the dramatic rise in energy prices after 1973.” The sign of the labor demand elasticity with respect; to the relative price of energy (treated as exogenous) depends on whether labor and energy are complements or substitutes in production. Further, a time trend is added to each equation to capture any deterministic forces left unaccounted for by the model.” The ‘first-stage’ regressions use transitory defense purchases, real wealth and the relative price of processed fuels and lubricants along with a time trend as the exogenous and predetermined variables.
“This annualized average of the three-month bill rates is used in the aksrn~c of onr-yc;tr bill:rates over the earher part of the sample period. “See King and Tatom and their references for additional discussion and cviclencc. 131n the labor demand function, the time trend accounts for both technological change and baseline growth in the net capital stock. The Bureau of JSconomicAnalysis’s measure of the net non-farm private capital stock was included as an additional explanatory variable but was tnsignjticant. One might expect trouble with this capital stock measure since the BEA consteucts its series under the assumption that annual depreciation is a constant percentage of the existing stock whereas our model views depreciation as varying directly with the firm’s choice of capital usage. u5, the BEA’s net capital stock measure is biased in that it understates (overstates) the true depreciation of thy capital stock during years of high (low) utilization. creasur)
77
Estlmaciesof the lahix market schedules ard rca wage rcdwcd-form:
1950- 1978.”
h@ne-tai! significance at the 0.05 test level. ’ Two-M significance at 0.05 test level. JNot significantly dilfercnt from zero at 0.05 tt’s*tlcvcl
The estimated labor demand function reported in row (1) corresponds closely to that predicted by the model of firm behavior developed in :iection 2. Movements in the real interest rate have significantly positive effects on the quantity of labor demanded. while the impact of the real \vage has the atike effect. Labor demand is negatively related to the relati\xz y suggesting that labor and energy are uomplementsr> input>. The point estimate of 2.86 for the elasticity of laf80r demand with respect to the real interest (significantly positive at the five percent lei,el) reveals tha[ firms increase ct:rrent labor demanded in response to anticipated intertemporal shifts in final product demand. The lower and upper limits of the ninety-ti1.c: percent confidence interval of our estimate of this key parameter are 0.12 ancl 5.60, respectively. The paint estimate of the elasticity of labor demand with nificantly negative at the five pcrwnt respect to the real wa level. The ninety~~ve interval for our estimate of tht: I&,-,demand real wage elasGcitl)- lies between the boundc#of -- 0.77 imd - 6.93.‘” The &mated ‘labor supply function for the private non-f;lrnl WI~V I’xted in row (2, of tnkle 2. Uoth the real interest rate and the real v;;lgt’ hale e, though imprecisely measured. cfkcts on labor hup I!. The imprlxkon of
28
J. J. Merri&
Jr., The uttrrcipurcd red irrtcrtw rute
these labor supply estimates is reflected in the facts that the ninety-five percent interval for the real interest rate elasticity lies between limits of - 0.68 and 12.22 while that of the real wage elasticity has bounds of - 1.81 and 11.63.r5 A minor, insignificantly negative real wealth effect is also present in the labor supply equation, Again, a time trend is included to capture the effects of any deterministic forces left unaccounted for by the model. Aside from the complete conformity of their estimated signs with those predicted by the theory, the most striking aspect of the labor market parameter point estimates reported here is the magnitude of the measured real interest rate elasticities for both labor demand and supply. Point estimates of 2.86 and 5.77, respectively, for the labor demand and supply elasticities with respect to the anticipated real interest rate might : Gemimplausibly high and may suggest that the model is m&specified.l6 Oln the other hand, an explanation of observed fiuctuations in employment and real output in terms of an intertemporal substitution model requires lablor market schedules that imply elastic responses to real interest rate changes. The highly elastic schedules estimated here seem to provide some support for the recent interest in using intertemporal channels to explain business cycle fluctuations. Finally, we turn to an analysis of the model’s prediction for the sign of the ‘cyclical’ pattern of real wages. Wow (3) of table 2 presents our estimate of the real wage reduced-form. Note that the relationship between the estimated reduced-form coefficient for the effect of transitory real government purchases on real wages (?rrr of section 5) and the estimated structural labor demand and supply elasticities with respect to the real interest rate reported in table 2 corresponds to the pattern predicted by the model as summarized in table 1. In particular, v;e find that a significantly positive labor demand effect exists, that the elasticities of labor demand and supply do not differ significantly in m;%gnitudefrom each other and that the coefficient for the transitory governmcnt purchases variable in the real wage reduced-form is not significantly different from zero. Thus, the evidence supports the model as providing a counterexample to Geary and Kennan’s conjecture that it is ‘unlikely that one could find omitted variables which influence both sides of the market in the manner necessary to produce the observed empirical results’ of statistical irkdependence of the real wage and employment time series.
confidence
I on with which the labor supply real intcrsst rate clusticify is cst:matcd ih 15The imprec’si disappointing though not completely unexpected in view of previous evidence. See 1 wa aud Rapping and also Hall.
‘(‘Data for 1948 and 1949 were originally included but subsequently dropped from the sample as they produced large errors in the real wage ‘first-stage’ and generated mllated (and insignificant) labor demand real interest rate and real wai;e elasticity estimates of 12.X and - 11.4, respectively. Mowever. the chosen 1950-1978 period does encompass the Korean and Vietnam war years in order to ensure sufficient variation in the transitory government defense expenditures variable. the model’s featured exogenous force.
9. J. Merrd
Jr..
The antrc-rpared red meresr rue
29
6. Chchding mm The analysis of ehe firm’s intertemporal maximization probiem presented
here
was
undertaken with the initial capital stock viewed as depreciable but fo that no sibihty existed for purchases of addition,aI units of newly-produced capi investment). The major problem posed by the introduction of a market for newly-pr~uc~ capital goods is that, within a perfect-market. complete info~nla~ion neoclassical model. investment demand is unambiguously negatir~ly related lo the anticipated real interest rate. Since our model implies that real interest rates vary procyclically, real investment must be cmmercyciicai - a prediction that is easily refuted by the data. Models capable of ~x~~aini~~/U&Ythe procyclical pattern in investment and procyclical capital utilizatnon may require a ‘time-to-build’ technology for capital accumulation as suggested by Barro and King (1982) or financial market imperfections reyulring firms to internally finance some part of their desired investment expenditures. Finally, it is important to emphasize that the ‘expansionary’ real interest rate effect on labor demand reported here within the capital utilization-depreciaGon framework is significant n3t only in regard to the cyclical pattern of real wages issue but also in providing an alternative to reliance on labor supply real interest rate effects as the transmission mechanism for intertemporal shocks. This point is of particular importance both because it lowers the magnitude of the labor supply real interest rate elasticity necessary to explain ohsened business cycle fluctuations and because of the generally poor results of attempts to empirically do‘;ument significant real interest rate effects on labor nonrtmewabie
supply.‘9
JMorE
B
30
J. J. Merrick, Jr,, The anticipated real interesl rule
Kuh, E., :1975, Employment, production functions and effective demand, Journal of Political Economy. *Dec. Lucas, R.E. and L. Rapping, 1970. Real wages, employment and inflation, in: Edmund Phclps, cd., Microeconomic foundations of employment and inflation theory (Norton, New York). Mishkin, !F.. 1980, The real interest rate: An empirical investigation, Paper presented at the Carnegie-Rochester Conference, Nov. Neftci, S., 1978, A time series analysis of the real wages-employment relationship, Journal of Political Economy, April. Sargent, I’., 1978, Estimation of #dynamiclabor demand schedules under rational expectations, Journal $I Political Economy, Dec. Tarshis. L., 1939, Changes in real and money wges, Economic Journal, March. Tatom, J., 1980, The problem of procyclical real wages and productivity, Journal of Political Economy. Taubman. P. and M. Wilkinson, 1970, User cost, output and unexpected price changes, in: Edmund Phelps, ed., Microeconomic foundations of employment and inflation theory (Norton, New York).