Unemployment and the Real Wage Gap:
A Reappraisal of the German Experience
By
Oliver Landmann a n d Jiirgen Jerger
C o n t e n t s : I. Introduction. - II. The Real Wage Gap: Concept and Measure- ment. - III. A Model of Capital Accumulation, Employment and the Wage Gap. - IV. Explaining the Falling Wage Share. - V. Explaining the Slowdown of Capital For- mation. - V I . Concluding Remarks. - Data Appendix.
he persistence o f h i g h unemployment i n E u r o p e continues to be a major concern o f theoretical and e m p i r i c a l m a c r o e c o n o m - ics [Dreze a n d Bean, 1990 b], I n particular, the challenge is to explain w h y b o t h reasonable d e m a n d g r o w t h a n d various favourable supply-side developments failed to b r i n g d o w n unemployment deci- sively i n the 1980s. W h e n unemployment rates first shot up a n d re- fused to return to earlier l o w levels i n the 1970s, a consensus o n the causes o f the p r o b l e m formed more easily. Adverse supply shocks and explosive wage g r o w t h were the essential elements o f the mainstream explanation, w h i c h heavily relied o n two key concepts: the NAIRU, a measure o f the unemployment rate consistent w i t h non-accelerating inflation, a n d the real wage gap, a measure o f the amount by w h i c h real wages supposedly exceed their e q u i l i b r i u m level. T h e c o l l i s i o n between the soaring wage aspirations o f workers and the diminished potential for real income g r o w t h pushed u p b o t h o f these measures [Bruno and Sachs, 1985].
In the 1980s, it became increasingly difficult to explain still higher unemployment rates along the same lines. A t first, the blame for the worsening employment picture c o u l d be put o n the severe demand contraction o f 1 9 8 0 - 8 2 , w h i c h added a layer o f K e y n e s i a n unemploy- ment to the inherited level o f classical unemployment [Bruno, 1986].
Remark: We acknowledge valuable comments on earlier drafts of this paper from participants at the M a y 1991 I E A conference "Open Economy Macroeconomics" in Vienna and at research seminars at the Universities of Hamburg and Munich. In particular, we thank S. Felder, F. X . H o f and E . Rysavy for pointing out an error in the specification of a preliminary version of our model.
I. Introduction
H o w e v e r , as h i g h unemployment persisted b e y o n d 1982 i n the face of recovering demand g r o w t h , the K e y n e s i a n explanation clearly lost appeal. B u t so d i d the classical unemployment hypothesis as real wages grew moderately at rates well below p r o d u c t i v i t y g r o w t h year after year.
T h e coincidence o f rising unemployment w i t h what appears to be wage m o d e r a t i o n prompts us to take another l o o k at the concept o f the real wage gap. Earlier authors such as Schultze [1987] have pointed out that changes i n the profit m a x i m i z i n g m i x o f factor inputs cast d o u b t o n the validity o f conventional measures o f the real wage gap as a n indicator o f an excessive real wage level and hence o f labour market d i s e q u i l i b r i u m . In this paper, we take the argument one step further b y offering a fully specified d y n a m i c m o d e l w h i c h endogenizes the choice o f factor inputs by firms and thus makes transparent how different shocks affect output, employment, investment, wages and factor shares i n different ways. T h e m o d e l pays particular attention to the role that capital a c c u m u l a t i o n has to p l a y i n a n explanation o f l a b o u r market developments, thus t a k i n g u p a theme emphasized by F i t o u s s i a n d Phelps [1988] i n their account o f the E u r o p e a n unem- ployment c o n u n d r u m .
T h e empirical sections o f o u r paper l o o k at the experience o f G e r - m a n y , confronting the predictions o f the m o d e l w i t h the most salient features o f m a c r o e c o n o m i c performance since 1970. T h e key relation- ships o f the m o d e l are estimated w i t h G e r m a n data for the period 1 9 6 1 - 9 1 . T h e m a i n indicators that w i l l concern us i n the subsequent analysis are c o m p i l e d i n Table 1 and F i g u r e 1. T h e figure charts the e v o l u t i o n o f o u r o w n measure o f the real wage gap (as estimated be- low) a l o n g w i t h the unemployment rate. E v i d e n t l y , the two variables m o v e d i n opposite directions for the most part o f the 1980s. T h e table summarizes some other distinct trends: the s l o w d o w n i n the average g r o w t h o f l a b o u r p r o d u c t i v i t y a n d real wages, the s l o w d o w n i n the pace o f capital a c c u m u l a t i o n as reflected b o t h i n the g r o w t h rate o f the capital stock a n d i n the investment ratio, a n d the m a r k e d rise o f the real interest rate after 1980.1
We n o w proceed as follows: I n Section II, we discuss some concep- t u a l issues relating to the real wage gap and present o u r o w n estimate.
1 The strong demand-led boom that the West German economy experienced in 1990-91 due to the unification generated a (temporary?) pick-up of real wage growth, employment growth and investment. However, the 1980-91 averages of these variables do not differ very much from their 1980-89 averages, in particular as they are com- pared with their pre-1980 values.
Figure 1 - The Wage Gap (left scale) and the Unemployment Rate (right scale) in Germany, 1961-1991
1.10-, R 9
0.96-1 , , , , , , , P , , , , , , , , ! , ,—, , , , ,—, , , , , _ 1961 1964 1967 1970 1973 1976 1979 1982 1985 1988 1991
Table 1 - Selected Economic Indicators for Germany, 1961-91
Variable 1961-1973 1974-1979 1980-1991
Unemployment rate* 0.8 3.5 6.6
G N P per hour workedb 5.1 3.6 2.0
Real wages per h o u rb 5.2 2.9 1.6
Capital stock b 5.6 3.6 2.8
Net investment
aggregate economyc 21.4 13.5 10.2
private sector0 16.6 9.5 7.8
Real interest rated 2.8 3.2 4.6
* Average level in per cent. - b Per cent change per annum. - c A s per cent of Net National Product ( N N P ) . - d Nominal interest rate minus G N P inflation rate;
average level in per cent.
Source: See data appendix.
O u r m o d e l is introduced i n Section III. Section I V empirically investi- gates the implications o f the m o d e l for the time path o f the l a b o u r share a n d the real wage gap. Section V is concerned w i t h the slow- d o w n o f capital f o r m a t i o n . Section V I concludes.
II. The Real Wage Gap: Concept and Measurement
T h e concept o f the real wage gap is intended to indicate the a m o u n t by w h i c h the prevailing real wage exceeds the level consistent w i t h full employment. T h e standard procedure to construct such an indicator is to choose a base p e r i o d i n w h i c h the economy was near full employment a n d for w h i c h the real wage gap is set equal to a benchmark value. N e x t , the hypothetical rate o f real wage growth that w o u l d have been feasible at continuous full employment is estimated a n d c o m p a r e d w i t h the rate actually observed [see e.g. Sachs, 1983;
B r u n o a n d Sachs, 1985]. T h e "feasible" g r o w t h rate o f real wages ob- viously depends o n the pace o f an economy's p r o d u c t i v i t y advance.
H o w e v e r , it has soon been realized that the actual g r o w t h rate o f l a b o u r p r o d u c t i v i t y is a p o o r p r o x y for the feasible g r o w t h rate o f real wages i f unemployment is not constant. T h e reason is that l a b o u r productivity endogenously responds to real wage changes as firms move a l o n g their l a b o u r d e m a n d schedules. D e p e n d i n g o n the elastic- ity o f l a b o u r demand, any excess real wage g r o w t h w i l l appear at least in part to " p a y for itself".
T h e p o i n t can be seen by considering a C E S representation of the p r o d u c t i o n process w h i c h relates output Y to the capital stock K, l a b o u r input N a n d time t:
Y- F ( X ,N , t ) = A[b{Ntexp(Ar)}'*
+ (l-b){Kttxp(tit)}-°]-lle- (1) T h e parameters X a n d \i denote l a b o u r augmenting a n d capital aug-
menting technical progress, respectively. F o r reasons that w i l l become clear below, the specification of technical progress is sufficiently gen- eral to leave open the possibility of non-neutral progress.2 W i t h c o m - petitive firms, the real wage W must equal the m a r g i n a l product of l a b o u r :3
W= bA~~eexp(-gAt)( Y/N)1 +« . (2)
S o l v i n g for the l o g of the average product o f l a b o u r (and denoting logs by lower-case letters), we get
y - n = a0 4- a(w-h) + It. (3)
2 The wage gap literature typically assumes Hicks-neutrality [see e.g. Schultze, 1987].
This corresponds to the special case A—y. in our formulation.
3 Allowing for monopolistic deviations from the benchmark case of perfect competi- tion would add a constant term (related to the price elasticity of demand). Since none of our results depends on variations in the degree of monopoly power, we ignore this factor throughout.
T h i s equation relates l a b o u r p r o d u c t i v i t y to the real wage and to labour-augmenting technical progress ( a0 is a constant; a is the elastic- ity of substitution, defined by (1 M o r e precisely, l a b o u r p r o - ductivity grows at the trend rate X as l o n g as the real wage grows at the same rate. If real wage g r o w t h deviates from this trend rate, productivity g r o w t h deviates i n the same direction depending o n the elasticity of substitution. I n the l i m i t i n g case o f the C o b b - D o u g l a s p r o d u c t i o n function ( o - = l ) , p r o d u c t i v i t y moves one-to-one w i t h the real wage so that any real wage g r o w t h appears "justified" ex post by the resulting p r o d u c t i v i t y increase.4 T h e trend deviation of the real wage, w — Xt, is what G o r d o n [1988, p. 287] has called the "adjusted wage gap". B y relating the real wage to trend productivity rather than actual productivity, this measure is presumed free of any bias stem- ming from endogenous p r o d u c t i v i t y changes. W e can rewrite (3) so as to make p l a i n h o w the adjusted wage gap is related to the unadjusted wage gap, where the latter is simply (an index of) the wage share i n national income:
w + n - y = - a0 + ( l- a ) ( w - X t ). (4)
In order to calculate the adjusted wage gap, we estimate (3) a n d (4) using quarterly data from the p e r i o d 1961:1 to 1991:4. T h e equations are estimated i n level form a n d the time series involved are tested for the property of cointegration. T h i s test indicates whether the long-run
" e q u i l i b r i u m " relationship between output, employment a n d the real wage, w h i c h is i m p l i e d by the o p t i m i z i n g behaviour of firms, is sup- ported by the d a t a .5
C o i n t e g r a t i o n is o n l y defined for variables of the same order of integration. Therefore, it is necessary to determine the order of integra- tion of the time series before cointegration diagnostics are used for the regressions. W e employ the methods suggested by Sargan a n d B h a r - gava [1983], P h i l l i p s [1987], P h i l l i p s a n d P e r r o n [1988] a n d Stock a n d Watson [1988]. T h e first one is based o n the D u r b i n - W a t s o n statistic ( S B D W ) , the second is a modification of the augmented D i c k e y - F u l l e r [1979,1981] test a n d includes a constant, a time trend a n d 4 lags of the differenced variable ( D F / P P ( 4 ) ) . F i n a l l y , the S t o c k - W a t s o n test also
4 This observation has been put forward as a principal objection against productivity- related wage guidelines; see Hellwig and Neumann [1987].
5 See Engle and Granger [1987] for an exposition of the methodology. The presence of cointegration also justifies more confidence in the quality of estimates involving non- stationary variables than traditional econometric theory would imply [Stock, 1987].
Table 2 - Integration Diagnostics
Variable S B D W D F / P P ( 4 ) StWa
Variable
level Alevel level Alevel level Alevel (W>N)/Y
w+n—y w k-n y-n
*** The null Appendix.
0.183 2.407*** » 2 . 4 7 5 -14.077*** -7.509 -175.87***
0.185 2.409*** -2.493 -14.125*** -7.531 -149.06***
0.002 1.914*** -1.122 -12.960*** - 1 . 1 0 2 -141.33***
0.002 2.436*** - 0 . 1 3 6 -17.306*** -0.665 -158.69***
0.002 2.451*** -1.116 -15.952*** -1.301 -155.39***
is rejected at the significance level < 1 per cent. F o r the data see the
includes the intercept a n d a trend, thus the g}-test (in the symbols of Stock a n d W a t s o n [1988]) is used (StWa).
T h e procedures test the n u l l " r a n d o m w a l k " (with drift a n d trend) against the alternative hypothesis of a stationary process. T h e results for levels a n d first differences are presented i n Table 2 .6 It is evident that a l l time series to be used are integrated of the order one.
F o r the purpose of estimation, (3) and (4) are written as follows:
y - n = a0 + axw + a2t + a3t + C0>-y*) (3') w + n - y = b0 + biw + b2t + b3x + C ( y - y * ) . (4') W i t h y * denoting the l o g of potential real G N P , (y—y*) captures the
cyclical sensitivity of p r o d u c t i v i t y and the wage share.7 B o t h regres- sions have been r u n w i t h a n d without this cyclical adjustment (col- umns 2 and 1 i n Table 3, respectively). Technical progress is assumed to be exogenous a n d is captured by trend terms i n the usual manner.
t denotes a time trend for the whole sample, whereas T is set equal to zero from 1961:1 through 1973:4 and increases by one unit per quarter thereafter. Thus, the equations allow for a break i n the rate of trend productivity growth after 1973. The rates are denoted by Xx (1961 — 1973) a n d X2 (1974-1991), respectively.
6 Besides the wage, the wage share and the average product of labour which appear in logs in (3) and (4), Table 2 also displays the integration diagnostics for some variables which will be used below.
7 Potential output was calculated from our database (see Appendix) along the lines proposed by the Sachverstandigenrat [1992, p. 259].
Table 3 - Estimates of (3') and (4')
(3') (40
Dependen y-n
t variable
w + n— y
(1) (2) (1) (2)
c R2 D W D F A D F ( 4 ) Note: <r, kx an T. - t-statistics tion in a setti variables are c see the Appen
- 0 . 0 1 4 - 0.016 -0.020 - 0.023
0.438 0.370 0.305 0.181 0.013 0.013 0.012 0.012 0.007 0.007 0.006 0.006
0.273 0.501 0.998 0.998 0.650 0.832
0.737*** 0.860 0.510*** 0.677 -5.253*** -4.193***
-3.231** -3.356**
id k2 are reported as implied by the estimated coefficients of w91 and are not reported, because they do not converge to a limiting distribu- ng with non-stationary variables [cf. Phillips, 1986]. - ***,*•; The
ointegrated at the 1 and 5 per cent level, respectively. - For the data dix.
T h e estimated coefficients translate i n t o the technical parameters of (3) a c c o r d i n g to
<x0 = aQ a = ai Xx = a2/(l-ax) k2 =(a2 + a3)/(l -ax)
and of (4) a c c o r d i n g to
x0 = -b0 a = l ~ bx Xx = - b2/ bx X2 = -{b2 + b3)/bx. T h e cointegration diagnosis is based o n the D u r b i n - W a t s o n coeffi- cient ( S B D W ) , the (simple) D i c k e y - F u l l e r test ( D F ) a n d the augmented D i c k e y - F u l l e r test ( A D F ( 4 ) ) .8 T h e results are s u m m a r i z e d i n Table 3.
N o t i n g that the parameters are reasonably stable across specifica- tions, we can d r a w the following conclusions from these estimates:
8 Our application of the cointegration technique is somewhat peculiar in that the equations include deterministic trend terms. The trend term, suggested by theory to capture the effects of technical progress, is, of course, non-stochastic, and thus falls outside the concept of integratedness. Nevertheless, cointegration can still be inter- preted as indicating the stationarity of the residual error and thus serves us as a means of regression diagnostics. The property of cointegration in this case is defined between the deterministic-trend-corrected L H S and the remaining R H S variables.
(a) In line with most previous w o r k , we find a n elasticity of substi- t u t i o n well below u n i t y .9 B y i m p l i c a t i o n , the adjusted wage gap gener- ally moves i n the same direction as the p l a i n wage share.
(b) T h e cyclical p r o x y enters the equations w i t h the expected sign, reflecting the pro-cyclical behaviour of p r o d u c t i v i t y and the corre- s p o n d i n g counter-cyclical behaviour of the wage share.
(c) T h e significant difference between kx a n d X2 reflects the well- k n o w n s l o w d o w n of trend p r o d u c t i v i t y g r o w t h i n the mid-1970s. E x - perimentation w i t h another d u m m y for the 1 9 8 0 - 9 1 p e r i o d was un- successful (confirming a similar result obtained by G o r d o n [1988]).
T h i s suggests that the noticeable s l o w d o w n of actual productivity g r o w t h i n the 1980s as c o m p a r e d w i t h the 1970s s h o u l d not be inter- preted as another structural break, but as an endogenous response to some force w h i c h simultaneously depressed real wage growth. A s we w i l l argue below, this force was the s l o w d o w n of capital d e e p e n i n g .1 0 (d) T h e cointegration diagnostics indicate the presence of cointe- gration for b o t h e q u a t i o n s1 1 a n d thus justify some confidence i n the existence of a long-term relation l i n k i n g output, employment and the real wage. I n this sense, the data d o not refute the n o t i o n that firms operate o n their neoclassical labour-demand schedules i n the l o n g run.
To calculate the adjusted wage gap index, we subtract the esti- mated trend productivity term [Xxt + (k2 — k^x] from the (log of the) actual real wage w. The series plotted i n the top panel of F i g u r e 1 is based o n an annual growth rate of trend productivity a m o u n t i n g to 4.8 per cent from 1961 to 1973 and 2.4 per cent from 1974 to 1991, as i m p l i e d by the regression results for equation (4') i n Table 3. Evidently, the wage gap rose substantially i n the years after 1969, reflecting the abrupt acceleration of real wage growth (the "wage explosion") i n that period. F r o m 1977 to 1991, i n contrast, the real wage level increased at o n l y about half the rate of trend productivity growth, thus d r i v i n g d o w n the wage gap index well below unity (the 1961 benchmark).
9 Our estimated a is particularly close to McCallum's [1985, p. 446]. Entorf et al. [1990]
estimate a value of 0.3 using the same technology specification with annual data from 1970-1986 for the private sector in Germany.
1 0 According to our derivation of (3), and contrary to Gordon's [1988, p. 286] pre- sumption, X does not pick up changes in the capital-labour ratio.
1 1 Cointegration tests apply only to regressions without (y—y*). The cyclical proxy is stationary by construction, so cointegration in the equations which include this term is ill-defined.
III. A Model of Capital Accumulation, Employment and the Wage G a p1 2
O u r next task is to develop a theoretical framework which allows us to explain variations i n the level of the real wage gap and to relate them to changes i n other macroeconomic variables. I n particular, we wish to show h o w a sustained rise i n unemployment can be associated either w i t h an increasing real wage gap (as i n the 1970s) or w i t h a decreasing real wage gap (the experience of the 1980s). O u r m o d e l abstracts from monetary and other demand-side disturbances that shape the cyclical behaviour of the economy. T h e focus is entirely o n the longer-term interaction of unemployment, the wage gap, wage setting behaviour and capital formation. T o simplify the exposition, the theoretical analysis i n this section also assumes away autonomous productivity change due to technical progress. I n terms of the notation introduced i n the last section, this amounts to k — /j = 0 so that the adjusted real wage gap index can be identified w i t h the real wage itself.
A n o t h e r i m p l i c a t i o n of this simplifying assumption is that the capital stock and the capital-labour ratio are stationary i n e q u i l i b r i u m .1 3 F i r m s are assumed to face a n exogenous real w o r l d interest rate and to operate o n competitive product m a r k e t s .1 4 T h e y choose their l a b o u r input as well as their real investment spending over time so as to m a x i m i z e the present value of cash flows V0:
V0^][F(KnNt)^WtNt-c(4>t)Kt]txp(^Rt)dt (5) o
subject to
Kt = dKt/dt = Kt(<Pt-S), where
K: C a p i t a l stock N:
W: R e a l wage c:
$ = I/K I:
R: R e a l interest rate <5:
(6)
L a b o u r input
Installation cost of capital goods Real investment spending (gross) P r o p o r t i o n a l rate of depreciation.
A dot over a variable denotes its derivative w i t h respect to time.
F is assumed to be a well-behaved constant returns to scale produc-
1 2 The model of this section is very similar in spirit to the one in Burda [1988J.
1 3 Alternatively, changes in these variables should be interpreted as changes relative to the respective trend paths.
1 4 Nothing of substance would change i f we allowed for some price-setting power on the part of firms.
t i o n function. F o l l o w i n g standard investment theory [e.g. B l a n c h a r d and Fischer, 1989, p. 58], we assume a convex cost function for the installation of capital goods, i.e. c' > 0, c" > 0. T h e behavioural i m p l i c a - tions of this o p t i m i z a t i o n p r o b l e m can be derived i n the usual way by setting up the current value H a m i l t o n i a n H a n d establishing the first- order c o n d i t i o n s :1 5
H = F ( K , N) -WN- c($)K + qK{<P-S) (7)
dH/dN = F2{K,N)-W=0 (8)
dH/dl = - c'($) + g - 0 (9) QH/dK = FX(K, N) - c(#) + q($-S) = Rq-q, (10)
where
q: Costate variable (shadow price of capital)
Ft: P a r t i a l derivative o f F with respect to the i-th argument.
T h e o p t i m a l i t y c o n d i t i o n (8) corresponds to equation (2) above. It i m p l i c i t l y shows l a b o u r demand as a function of the capital stock a n d the real wage. E q u a t i o n s (6), (9) and (10) together determine the dy- namics of capital a c c u m u l a t i o n a l o n g the lines of Tobin's q theory of investment. Instead of the usual (<2,K)-format, we choose here a ( $ , K ) - representation to m a k e the time path of investment m o r e readily visible. Substituting equation (9) and its time derivative i n t o equation (10) , we get
<P - 1 [&(R + 6-#) + c(#) - FX{K9N)]. (11)
c
W e cannot analyze the dynamics of the system formed by (6) a n d (11) without t a k i n g into account the interdependence o f capital forma- t i o n a n d the l a b o u r market. T h e m a r g i n a l p r o d u c t i v i t y o f capital Ft depends o n l a b o u r input JV ( F1 2> 0 ) . E m p l o y m e n t , i n turn, is deter- m i n e d o n the l a b o u r market where the l a b o u r d e m a n d of firms as i m p l i e d by (8) depends o n the size of the capital stock. T o complete the description of the l a b o u r market, we assume wage-setting to be gov- erned by an equation o f the following form:
W=MN/N*,z)9 *»*2>Q (12)
where
N * : L a b o u r force (exogenous)
z: Vector of exogenous variables relevant to wage-setting.
Hereafter, time subscripts will be dropped where dispensable.
We d o not provide m i c r o e c o n o m i c foundations for this relation- ship, but we note that it is consistent w i t h a number of l a b o u r market models such as m o n o p o l y u n i o n models, bargaining models, efficiency wage models o r insider-outsider models (see also the discussion i n L i n d b e c k [1992]). Besides the unemployment rate, these models sug- gest various other variables that m a y affect wage-setting. O b v i o u s examples are t o t al factor productivity, unemployment benefits, the terms of trade, taxes and u n i o n militancy. Such variables are captured by the exogenous vector z.
E q u a t i o n s (8) and (12) together determine the e q u i l i b r i u m levels of employment and the real wage. S o l v i n g for N and W we get
N = g(K9N*9z) gu g2 > 0, g3 < 0 (13)
W=h(K,N*9z) hl9h3>09h2<0. (14)
T h i s is a n e q u i l i b r i u m i n the sense that the real wage outcome intended by wage-setters according to (12) is consistent w i t h the de- m a n d price of l a b o u r derived from (8). Since the wage bargain is cast in n o m i n a l terms, actual outcomes may differ from the e q u i l i b r i u m solution due to expectational errors and n o m i n a l rigidities [Blanchard, 1990]. A n y such d i s e q u i l i b r i u m sets i n m o t i o n an accelerating wage- price spiral w h i c h can go o n as l o n g as authorities are prepared to provide the necessary monetary a c c o m m o d a t i o n . A s s o o n as n o m i n a l demand g r o w t h is adjusted, however, so as to end the wage-price spiral, output and employment are eventually forced back to their e q u i l i b r i u m levels [ L a y a r d and Bean, 1989]. Since the present paper is not concerned w i t h these transitory monetary disequilibria, any subse- quent reference to employment i n this section is to e q u i l i b r i u m em- ployment as determined by (13). T h e corresponding unemployment rate (N*-g)/N* is what L i n d b e c k [1992] has termed the Q E R U ("quasi-equilibrium rate of unemployment") or what i n a P h i l l i p s - curve context w o u l d be referred to as the N A I R U .
After substituting (13) into (11), w h i c h gives
# = i [cr(R + 6-#) + c(#) - Ft{K9g(K9N*9z)}] 9 (11') c
We can proceed to the analysis of the j o i n t dynamics of capital accu- m u l a t i o n and employment. F i g u r e 2 displays the relevant phase d i a - gram. T h e K = 0 locus depicts the equilibrium c o n d i t i o n for the capital stock derived from the state equation (6). It is vertical at #=<5. The
* = 0 locus is the c o n d i t i o n for the investment-capital ratio to remain
F i g u r e 2 - The Laws of Motion for Investment and the Capital Stock
stable. T o determine its slope, we set <P = 0 i n (11') a n d totally differen- tiate with respect to K a n d 4>. W i t h the n o r m a l i z a t i o n JV* = 1, the equations (8), (12) and (13) i m p l y g1=F2l/(xl/1 — F22) so that the slope is given by
W i t h constant returns to scale, the denominator of (15) is negative as l o n g as \l/x > 0 . T h e numerator is positive i f the real interest rate is positive (which we assume) and i f the system is close enough to its e q u i l i b r i u m point where <£ = <5. Thus, the # = 0 locus is depicted as d o w n w a r d s l o p i n g .1 6 T h e direction of the arrows of m o t i o n can be derived from (6) a n d (11') i n the usual way. T h e overall e q u i l i b r i u m of the system is obviously a saddlepoint. S P is the unique stable path leading to this e q u i l i b r i u m . T h e transversality c o n d i t i o n
l i m qtQxp(-Rt) = 0 (16)
ensures that the system always converges to its e q u i l i b r i u m along this stable path.
We are n o w i n a p o s i t i o n to analyze the d y n a m i c consequences of exogenous shocks. T h e wage e x p l o s i o n of the early 1970s can be
dK
d $ (15)
1. A D o m e s t i c W a g e S h o c k
1 6 In the limiting case of ^ =0, i.e. complete real wage rigidity, the # = 0 locus is verti- cal and no equilibrium exists. In Figure 2, the ^ = 0 locus is drawn as a straight line and thus must be interpreted as a linear approximation of (15) around the steady state.
Figure 3- A Sequence of a Wage Shock and an Interest Rate Shock:
The Response of Investment, the Capital Stock, the Real Wage and Employment
represented, i n terms of o u r model, as an abrupt increase i n z. Inspect- ing ( 1 1 ' ) - a n d taking account of Fx 2 g3 < 0 - we can see that this shock displaces the $ = 0 locus d o w n w a r d . I n panel a) of F i g u r e 3, point A represents the initial e q u i l i b r i u m p o s i t i o n of the system. T h e d o w n - w a r d shift of the $ = 0 locus (which is not depicted) is assumed to give rise to a new long-run e q u i l i b r i u m at point C w i t h a lower capital stock. Since the capital stock is predetermined at each point of time, the new e q u i l i b r i u m cannot be reached immediately. Rather, the i m - pact effect of the shock is to reduce investment sharply so as to place the system o n the stable path S P j (point B). O v e r time, the capital stock gradually adjusts d o w n w a r d while investment recovers so far as to reestablish the i n i t i a l level of $ at the new e q u i l i b r i u m point C .
T o make clear what is going o n behind the scenes of this adjust- ment process, we have attached two further panels to F i g u r e 3. P a n e l c) depicts the interaction of labour demand and wage-setting behav- iour as described by (8) and (12). A g a i n , point A is the initial equilib-
r i u m . A s the push for higher wages sets i n , the wage-setting schedule shifts up from W S0 to W SX. G i v e n the inherited capital stock K0, the real wage rises to Wx. E m p l o y m e n t must fall to Nt i f the wage-price spiral resulting from the wage shock is to be contained. T h i s is not the end of the adjustment process, however. Since the m a r g i n a l produc- tivity of l a b o u r depends o n the size of the capital stock, the labour demand curve gradually shifts to the left as the disinvestment process is t a k i n g its course. A s a consequence, employment is further de- pressed to N2 while at the same time the i n i t i a l real wage gain is c o m - pletely eroded. It m a y appear p a r a d o x i c a l that the long-run effect of the drive for higher real wages is to leave the real wage level unaffected.
B u t that is what the constant returns to scale technology a n d the endogenous capital stock imply. A s B l a n c h a r d [1990, pp. 7 5 - 7 6 ] has put it, the l o n g - r u n l a b o u r demand curve is h o r i z o n t a l [see also Bean, 1989].
T h e i m p l i e d co-movement of the capital stock and employment - a n d hence the capital-labour ratio - is illustrated i n panel b). After an i n i t i a l rise i n the capital-labour ratio due to the loss of employment between points A a n d B , a mutually reinforcing contraction of capital and l a b o u r input leads to a new e q u i l i b r i u m at p o i n t C where the orig- i n a l intensity is again supported by the o r i g i n a l factor price r a t i o .1 7
T h e m o d e l tells a story w h i c h is roughly i n line w i t h the facts presented i n the i n t r o d u c t i o n . T h e pattern of simultaneously rising unemployment a n d real wages depicted by the transition from p o i n t A to p o i n t B i n panel c) of F i g u r e 3 m i r r o r s the G e r m a n experience - and, for that matter, the experience of many other E u r o p e a n countries - i n the first half of the 1970s when the N A I R U by most accounts rose from a r o u n d 1 per cent to a r o u n d 4 per cent [see e.g. F r a n z , 1987], T h i s was the p e r i o d that revived the interest i n the n o t i o n of classical u n - employment a n d led to the construction of wage gap indices. O f course, the exact t i m i n g of actual output and employment develop- ments was strongly influenced by the monetary disturbances which supervened o n the real forces analyzed above. Whereas the increased wage pressure dates back to the late 1960s, it was at first deflected into rising inflation rates by a highly a c c o m m o d a t i n g stance of n o m i n a l demand management. Therefore, the plunge of investment was de- layed a n d actual unemployment d i d not catch u p w i t h the rising
1 7 Note again that the model portrays a stationary economy. A l l the results carry over to a growing economy, however, if the variables are reinterpreted as trend-adjusted (see Section IV for such a reinterpretation).
N A I R U until 1974/75 when the monetary a c c o m m o d a t i o n of inflation was discontinued.
T h e wage gap began to decline i n the second half of the 1970s.
However, employment g r o w t h still fell short of its pre-recession rate and unemployment remained stubbornly high. Investment remained depressed. The failure of a falling wage gap to b r i n g d o w n unemploy- ment is not surprising i n view of the properties of the transition path from p o i n t B to point C i n F i g u r e 3. There is no simple a n d stable relationship between real wage and unemployment once the endoge- nous adjustment of the capital stock is taken into account.
2 . A F o r e i g n I n t e r e s t R a t e S h o c k
T o portray the situation o f the early 1980s as a case of a pure real interest rate shock is clearly an oversimplification. In particular, the rise i n w o r l d interest rates coincided w i t h the second o i l price shock and with a sharp appreciation of the U . S . dollar. G e r m a n y , along w i t h most other E u r o p e a n countries, thus experienced a deterioration of its terms of trade w h i c h by itself contributed to inflationary pressure a n d to a further increase i n the N A I R U . However, because this disturbance was not as pronounced as the wage shock of the early 1970s, and also because it was subsequently reversed, we neglect it i n the following analysis and instead focus o n the consequences of the more sustained increase i n the real rate of interest.
We t u r n again to F i g u r e 3 a n d consider an i n i t i a l e q u i l i b r i u m depicted by point C i n each of the three panels (thus assuming, for the sake of simplicity, that a l l variables, i n c l u d i n g the capital stock, have completed their adjustment to the previous shock). A rise i n the real interest rate lowers the e q u i l i b r i u m capital stock. I n the (#, K) phase diagram, the * = 0 locus thus shifts d o w n once more as can be verified from equation (11'). T h e l o n g - r u n e q u i l i b r i u m position of the system moves further d o w n a l o n g the K—0 locus to point E i n panel a) of Figure 3. T h i s e q u i l i b r i u m can o n l y be reached a l o n g the new stable path S P2. Investment must fall o n impact so as to place the system o n this p a t h at point D . T h e capital stock thus gradually adjusts d o w n - w a r d to its new o p t i m a l level K2.
A s far as capital formation is concerned, the real interest rate shock evidently generates the same type of d y n a m i c response as the wage shock. T h e l a b o u r market response, i n contrast, is different. Since the interest rate does not directly enter the wage-setting equation or the labour demand equation i n this m o d e l , neither the natural employ-
merit rate n o r the wage rate are affected o n impact. A s the capital stock adjusts over time, however, l a b o u r demand falls. T h i s is represented by the displacement of the Nd schedule from N{ to N\ i n panel c) of F i g u r e 3. A s a result, the real wage and employment continue to de- crease together a l o n g the wage-setting curve W Sl 5 from point D ( = C ) to point E . P a n e l b) again illustrates the co-movement of the capital stock, employment and output. W h i l e b o t h factor inputs fall i n the course of the adjustment process, the capital-labour ratio must also decline i n response to the increased cost of capital and the falling real wage. Therefore, the new e q u i l i b r i u m point E is located o n a lower ray from the origin than the previous e q u i l i b r i u m C i n panel b).
T h e theoretical analysis of the interest rate increase again yields predictions that appear to be b r o a d l y i n line with the facts. T h e i n - vestment weakness predicted by the m o d e l is one of the most salient features of G e r m a n y ' s macroeconomic performance d u r i n g the 1980s.
T h r o u g h o u t the decade, the net investment ratio never recovered from the trough of the 1981/82 recession to anywhere near the already de- pressed level of the 1970s. O f course, the capital-labour ratio d i d not literally fall as it does i n o u r stationary-model economy. B u t its rate of g r o w t h fell to a post-war l o w w h i c h was widely seen as a major cause of the continued s l o w d o w n of l a b o u r p r o d u c t i v i t y growth. D i s - cussing the consequences of this investment s l o w d o w n , the O E C D [1988, p. 53] aptly diagnosed a "vicious circle" of sluggish capacity g r o w t h a n d j o b creation i n w h i c h "weak economic g r o w t h eventually began feeding u p o n itself". T h e m u t u a l l y depressing effects of falling output a n d employment o n investment a n d of inadequate capital formation o n the demand for l a b o u r are indeed at the very core of the contractionary adjustment process portrayed i n F i g u r e 3.
D u e to o u r n o r m a l i z a t i o n of the total l a b o u r force ( N * = 1), the fall i n N is to be interpreted as a fall i n the employment rate, not neces- sarily i n the absolute v o l u m e of employment. A s a matter of fact, employment g r o w t h picked up somewhat after 1983, but not enough to keep up w i t h the expanding supply of l a b o u r .1 8 T h e coincidence of a sharply falling wage gap a n d a n increasing unemployment rate w h i c h has done so m u c h to discredit the classical-unemployment hypothesis and the t r a d i t i o n a l wage-gap analysis i n the 1980s is a
1 8 The effects of the rise in the labour force are ignored in this paper; see, however, the discussion in Landmann and Jerger [1993].
straightforward property of the transition from point D to point E i n panel c) of F i g u r e 3. A g a i n , the time path of actual unemployment differed from the gradual upward-creep which the m o d e l predicts for the N A I R U . T h e actual unemployment rate shot up i n 1 9 8 1 - 8 3 under the influence of a stern anti-inflationary monetary policy and was kept high for a n extended period of disinflation d u r i n g w h i c h most esti- mates of the N A I R U were gradually revised upwards [Franz, 1987].
W h i l e this behaviour of the N A I R U may give the appearance of hysteresis, it is also consistent w i t h the disinvestment mechanism de- scribed above. O f course, the actual empirical importance of this mechanism cannot be established by a rough c o m p a r i s o n of an ab- stract m o d e l w i t h the stylized facts. I n the next section, we therefore take a first step towards a more formal e m p i r i c a l underpinning of o u r story.
IV. Explaining the Falling Wage Share
T h e above analysis suggests that the concept of the (adjusted o r unadjusted) real wage gap is of little use i n spotting a real wage p r o b l e m o n the l a b o u r market. I n fact, the very n o t i o n of an "excessive real wage level" is ill-defined i n view of the endogenous determination of the real wage. M a n y writers have emphasized that the C E S technol- ogy (for <7^1) actually predicts such changes i n distributional shares as a consequence of changes i n the factor-price ratio and the capital- labour ratio even i f full employment is permanently maintained [e.g.
M c C a l l u m , 1985; K r u g m a n , 1987; Schultze, 1987]. A s G o r d o n [1988, p. 285] has put it: " W i t h a n elasticity of substitution between l a b o u r and capital below unity, the n o r m a l process of capital accumulation w o u l d be expected gradually to raise labour's share and measured wage gap indexes." B u t as a matter of fact, the capital-labour ratio continued to rise throughout the past decade i n the face of a substan- tial decline of the adjusted wage gap. Since the endogenous adjustment of the capital stock plays a central part i n our m o d e l of wage and unemployment dynamics, we n o w take up the question whether the observed time p a t h of the wage gap and the l a b o u r share can be ex- plained by the changing pattern of capital accumulation a n d employ- ment g r o w t h as our theoretical analysis implies.
A g o o d starting point for the e m p i r i c a l analysis is the quadratic a p p r o x i m a t i o n of the C E S function (1), first proposed by K m e n t a [1967]. W i t h a specification of technical progress as i n (1), this logarith-
m i c a p p r o x i m a t i o n is
y = a + [bX + (1 t + bn + (1 -b)k
-±eb(l-b)[k-n-(X-ii)t]2. (1')
H e r e again, y, k a n d n denote the log, respectively, o f real output, the capital stock and employment. T h e parameters have the same meaning as i n (1) above.
If l a b o u r receives its m a r g i n a l product, the l a b o u r share is equal to the partial elasticity of output w i t h respect to labour:
^ = W-N/Y = b + Qb(l-b)[k - n - (X-fi)t]. (17) on
T w o points emerge from (17). F i r s t , an increase i n the capital- l a b o u r ratio raises the l a b o u r share at any given time i f the elasticity of substitution is below unity ( o g > 0 ) as o u r estimates i n Section II suggest it is. Second, the time path of the l a b o u r share is not uniquely determined by the capital-labour ratio, but also depends o n the pace and the nature of technical progress. O n l y i n the special case of H i c k s - neutral progress (X=/*) w o u l d an o n g o i n g process of capital deepening inevitably result i n the ever-increasing l a b o u r share expected by G o r d o n . Since the recent fall of the l a b o u r share was accompanied by continued capital deepening, H i c k s - n e u t r a l i t y does not seem to be a particularly attractive assumption. Therefore, the estimation of (17) should a l l o w for a time trend. Initial testing indicated that a break i n the trend term as i n (3') and (4') is not significant. A linear time trend is sufficient. T h e regression was r u n b o t h w i t h a n d without a cyclical adjustment term £(y —y*). T h e results are given i n Table 4.
T h e cointegration satistics d o not contradict the j o i n t hypothesis, embodied i n (17), that firms operate b o t h o n a C E S p r o d u c t i o n func- t i o n a n d o n the derived l a b o u r demand curve i n the l o n g r u n .1 9 T h e capital-labour ratio enters w i t h the expected positive sign whereas the coefficient of the time trend is negative, thus reconciling the n o n - increasing l a b o u r share w i t h the o n g o i n g process of capital deepening.
T h e R H S of (17) essentially features the capital-labour ratio, adjusted
1 9 Admittedly, the relatively low R2 indicates scope for improving the specification with regard to the short-run dynamics. However, our interest here is limited to the long-run validity of the first-order condition (17) for which the cointegration diagnosis testifies in the positive.
Table 4 - Estimates of (17)
Dependent variable: W-N/Y
(1) (2) Constant
Coeff(k-n)
c ft2 D W D F A D F ( 4 )
Note: *, **; The variables a tively. For the data see the
0.603 0.605 0.181 0.174 0.011 0.011
-0.098
0.536 0.550 0.360* 0.338 -3.300*
-3.167**
re cointegrated at the 10 and 5 per cent level, respec- Appendix.
for a time trend [k — n—(A—//) t]. I n analogy to the adjusted wage gap, we refer to this variable as the adjusted capital intensity ( A D J C I ) . T h e upper panel of F i g u r e 4 plots A D J C I against the observed wage share (WS). I n contrast to the unadjusted capital-labour ratio, w h i c h kept growing i n absolute terms throughout the three decades under review, A D J C I fell substantially i n response to the l o w level of investment i n the 1975-1988 period. Thereby, it closely paralleled the declining wage share (WS) a n d the declining real wage gap (not shown i n F i g - ure 4, but depicted i n F i g u r e 1). T h i s correlation is what the theoretical model i n Section III predicts - i f we bear i n m i n d that A D J C I is the empirical counterpart of K/N i n F i g u r e 3 b.
O n e might object that it is i m p r o p e r to rely o n an exogenous time trend to square an increasing capital-labour ratio w i t h a falling wage share. However, A D J C I is closely related to the concept of capital per
"effective" worker, routinely used i n expositions of the S o l o w g r o w t h model w i t h labour-augmenting technical progress. A s the S o l o w model demonstrates, labour-augmenting technical progress causes a trend increase i n the capital-labour ratio even i n the absence of any extraneous wage pressure that might arise from l a b o u r market imper- fections. O u r specification differs from the scenario of the textbook model because S o l o w assumed / / = 0 a n d thus obtained a steady state with a constant capital-output ratio whereas G e r m a n y ' s capital-out- put ratio steadily crept u p w a r d w i t h a pace of 1.06 per cent p.a. from 1961 to 1991. T h i s is w h y o u r estimates i m p l y a higher trend growth
rate for the capital-labour ratio than for l a b o u r productivity (i.e. a higher value for A — \i i n (17) than for A i n (3)).
W h i l e the co-movement of the wage share a n d the capital-labour ratio fits our story well, it does not shed light o n the role of relative factor prices i n causing the observed relation. W e address this issue by noting that the first-order c o n d i t i o n which defines the o p t i m a l capital stock of firms can be derived from the p r o d u c t i o n function (1) i n analogy to equation (3) as follows:
y ~ * = To + <r(uc — iu) + lit, (18) where uc is the l o g of the user cost of capital.
Subtracting (18) from (3), we can relate the capital-labour ratio to the factor-price ratio:
k — n = a0 — y0 + <T(W — UC) + (1 — a){X — ^)t (19) or, equivalently:
k — n — {X — ii)t = a0 — y0 + <T[W — uc — (A —fi)t]. (19') T h e L H S of (19') is the adjusted capital-intensity A D J C I as ex-
plained above. T h e term i n brackets o n the R H S is the factor-price ratio, adjusted i n the same way. E q u a t i o n s (18), (19) and (19') represent steady-state relationships and d o not take into account the extended adjustment process w h i c h we have modelled above. Therefore, we d o not estimate these relationships. However, i n order to reach a first pass judgment o n the importance of relative factor prices, we have calcu- lated the adjusted factor-price ratio [w—uc—(X — fi)t], using the trend adjustment term (A —fi)t as reported i n Table 4. T h e resulting series, termed A D J R F C , is plotted against the adjusted capital intensity ( A D J C I ) i n the lower panel of F i g u r e 4. A s expected, the chart does not suggest a n excitingly close fit of the two series, but it demonstrates that the factor-price ratio, once it is adjusted for its secular trend growth, exhibits a noticeable d o w n w a r d tendency accompanying the extended decline of A D J C I . B o t h of the shocks, which we have discussed above show up i n the A D J R F C series: A r o u n d 1970, the ratio shot up as the wage explosion coincided w i t h an a c c o m m o d a t i n g stance of monetary policy, w h i c h kept the interest rate low. I n contrast, the subsequent fall of A D J R F C was particularly steep i n the 1 9 7 8 - 8 1 p e r i o d when the economy was hit b y the interest rate shock.
V. Explaining the Slowdown of Capital Formation
T h e theoretical a n d empirical results derived above emphasized the disinvestment process w h i c h was induced by the wage shock of the early 1970s as well as by the real interest rate shock a decade later. In this section, we take a closer l o o k at the causes of the s l o w d o w n of capital formation. A c c o r d i n g to (18), the e q u i l i b r i u m capital stock should be related to the level of output a n d the user cost of capital. We take i n t o account the gradual adjustment of the capital stock by a l l o w i n g for a lagged response of investment to changes i n output g r o w t h and user costs. A s s u m i n g K o y c k - d i s t r i b u t e d lags a n d follow- i n g a standard a p p r o a c h pioneered b y Bischoff [1971], we derive the following equation for the change i n the capital s t o c k :2 0
Akt = 0.070 + 0.059 Ayt - 0.014 uct + 0.885 Afcf_ x (20) (2.459) (2.744) ( - 2 . 4 1 1 ) (18.053)
R H O = 0.262 (1.029)
Estimation method: O L S with correction for first-order serial correlation (Hildreth-Lu search procedure, cf. e.g. Maddala [1977, pp. 277 ff.]).
Sample 1963-1991 R2: 0.961 SEE: 0.002 LM(4): 5.847
(t-statistics in parentheses; LM(4) refers to the Lagrange Multiplier Test for serial correlation.)
Since a l l variables i n (20) were found to be 1(0), the standard tests for significance are appropriate. U n l i k e some other studies of invest- ment, we find a significant role for the user cost v a r i a b l e .2 1 I n an attempt to identify the proximate causes of the slowing pace of capital formation, we perform t w o ex post simulations w i t h (20), b o t h for the p e r i o d 1 9 7 4 - 1 9 9 1 . F i r s t , we calculate a baseline path for the change
2 0 Note that the user cost variable appears in level form rather than as a first difference.
This specification results i f the lag structures of the response to changes in output and of the response to changes in the user cost are allowed to differ [Bischoff, 1971]. For other recent applications of BischofPs approach, see Clark [1979] and Corker etal.
[1989].
2 1 Because of data limitations, (20) was estimated with annual data for the capital stock of the aggregate economy. O f course, one could argue that only private-sector invest- ment should be made dependent on output growth and the capital costs. O n the other hand, the slump of output growth and the rise in the real interest rate importantly con- tributed to the perception, in the early 1980s, that the time path of Germany's public debt was unsustainable. This perception ultimately triggered the sharp cuts in public investment spending that became effective after 1982.
i n the c a p i t a l stock, assuming output g r o w t h a n d the user cost of capi- tal to have remained constant at their average values of 1 9 6 1 - 1 9 7 3 . In F i g u r e 5, this baseline s o l u t i o n is labeled S I M 1 . The fact that S I M 1 slopes moderately d o w n w a r d s indicates that the pace o f capital forma- tion up to 1973 was not sustainable even under the prevailing c o n d i - tions of that period. Presumably, some s l o w d o w n of investment was inevitable after a postwar transition p e r i o d i n w h i c h the capital-output ratio h a d to be restored to its e q u i l i b r i u m level.
T h e second simulated path of Afc, labeled S I M 2 i n F i g u r e 5, is based o n the same output g r o w t h as S I M 1 , but o n actual values of uc.
N o t surprisingly, S I M 2 does not depart substantially from S I M 1 until the r u n up o f real interest rates a r o u n d 1980. Whereas the shortfall of S I M 2 as against S I M 1 indicates the direct c o n t r i b u t i o n of the rise i n capital costs to the change i n investment, the discrepancy between the fitted A/c a n d S I M 2 must be attributed to the s l o w d o w n of output g r o w t h .2 2 O u t p u t growth appears quantitatively to be the more i m - portant factor for investment t h a n the user cost of capital, which is i n
2 2 In 1991, the difference between the baseline solution SIM1 and SIM2 accounts for 44.5 per cent of the difference between SIM1 and the fitted values for Ak.
line w i t h a n o v e r w h e l m i n g b o d y of evidence i n the literature. It should be kept i n m i n d , however, that output g r o w t h is not entirely a n auto- nomous determinant of capital formation. Q u i t e to the contrary, the m o d e l of Section III precisely predicts that a real interest rate shock m a y exert its contractionary effect o n the capital stock largely v i a an induced c o n t r a c t i o n of aggregate output. T u r n i n g once more to F i g - ure 3 (panel b) above, we recall that the assumed real interest rate shock lowers the capital stock from Kx to K2. A statistical decompo- sition as outlined i n this section w o u l d attribute most of the change i n the capital stock to the change i n output - w h i c h falls from Y2 to Y$
a n d thus warrants a lower capital stock, given the i n i t i a l capital- l a b o u r ratio. T h e change i n the user cost of capital, though it is the ultimate source of the entire disinvestment process, w o u l d not be credited but for the m i n o r movement to the new e q u i l i b r i u m capital- l a b o u r ratio a l o n g the Y3 isoquant. T h u s , a statistical decomposition based o n an equation such as (20) can at best provide a lower b o u n d for the fraction of the investment s l o w d o w n that is i n fact caused by the sustained rise i n the real interest rate.
VI. Concluding Remarks
U n e m p l o y m e n t i n G e r m a n y , as elsewhere i n E u r o p e , has increased dramatically between the early 1970s and the late 1980s. I n the 1970s, the mainstream view blamed excessive wage pressure. T h i s view made heavy use of the real wage gap measures w h i c h indicated that real wages were r u n n i n g ahead of (trend) productivity. I n the 1980s, when unemployment rose still higher while the real wage gap declined rapidly, the mainstream view was that excessive wage pressure could no longer be b l a m e d [see G o r d o n , 1988; Paque, 1990]. O u r analysis i n this paper has led us to two b r o a d conclusions: First, the real wage gap, as usually measured, is of little use as a n indicator of excessive wage pressure. Second, whereas the mainstream view of the 1970s nevertheless seems to be correct, the mainstream view of the 1980s is more dubious.
T h e basic argument u n d e r l y i n g o u r first c o n c l u s i o n is very simple:
Since the real wage is a n endogenous variable of the macroeconomic system, j o i n t l y determined by wage-setting a n d l a b o u r d e m a n d be- haviour, it cannot be expected to be related to employment i n any stable way. D e p e n d i n g o n whether exogenous shocks affect the l a b o u r market t h r o u g h the wage-setting schedule o r through the l a b o u r de- m a n d schedule, the real wage a n d the unemployment rate w i l l move
together or i n opposite directions. O u r explanation of why they m o v e d in opposite directions after the mid-1970s points to the role of the slowing capital formation.
T h e n o t i o n that E u r o p e a n unemployment m a y be related to insuf- ficient investment is not uncontroversial. It is dismissed out of h a n d by G o r d o n [1988, p. 278] w h o cited the 87.6 per cent increase i n Europe's capital-labour ratio from 1972 to 1986 as evidence of the contrary (for G e r m a n y , the figure is 78.6 per cent). However, once the capital- labour ratio is adjusted for its trend, w h i c h w o u l d n o r m a l l y be ex- pected to be increasing i n a g r o w i n g economy, we find a rather steep decline after 1975 (Figure 4 a, above). If the elasticity of substitution between capital a n d l a b o u r lies below unity, as most estimates i n c l u d - ing our o w n i m p l y , any reduction of the (trend-adjusted) capital- labour ratio must lower the wage share i n n a t i o n a l income a n d the (adjusted) real wage gap, w h i c h is what actually happened.
T h e pace of capital accumulation also plays a significant role i n the theoretical framework underlying the " E u r o p e a n U n e m p l o y m e n t Project" described i n D r e z e and B e a n [1990a]. I n fact, the G e r m a n contribution to the project [Entorf et al., 1990] presents empirical results which give strong support to the n o t i o n that a lack of produc- tive capacity limited employment growth i n G e r m a n y . T o be sure, whereas their approach emphasizes rationing phenomena stemming from demand a n d capacity constraints, we ignore such d i s e q u i l i b r i u m mechanisms and instead adopt an e q u i l i b r i u m perspective i n w h i c h the capital stock enters as a determinant of l a b o u r market e q u i l i b r i u m . Whenever the wage-setting process exhibits real wage resistance, as equation (12) of o u r m o d e l assumes, a d o w n w a r d shift of the l a b o u r demand schedule due to a fall i n the (trend-adjusted) capital-labour ratio inevitably translates i n t o rising unemployment.
Since we d i d not estimate a wage-setting equation, we cannot say how m u c h a d d i t i o n a l unemployment is i n fact explained by this mech- anism. W h a t we can say, however, is this: T h e disappearance of the G e r m a n real wage gap, though widely interpreted as evidence of
"wage moderation", is perfectly consistent with the view that the per- sistent h i g h unemployment of the 1980s results from a failure of the wage-setting process to adjust to a continued s l o w d o w n of feasible real wage growth.
A referee raised the question whether the strong investment per- formance of West G e r m a n y i n 1990/91 and the concomitant moderate rise i n o u r real wage gap measure might indicate a t u r n a r o u n d i n the trend of the preceding decade. A t the time of writing, it is too early to
tell - a l l the more so as the 1990/91 unification b o o m was followed by a deep recession. H o w e v e r , the events s u r r o u n d i n g the G e r m a n uni- fication demonstrate the force of our argument i n another, sad way.
T h e integration o f a seriously undercapitalized economy meant an ab- rupt fall i n the capital-labour ratio for the F e d e r a l R e p u b l i c o f G e r - m a n y as a whole. B u t wage-setters, striving for a q u i c k e l i m i n a t i o n of the East-West wage differential showed very little willingness to take this fact i n t o account. Thereby, they caused a new and presumably persistent unemployment p r o b l e m affecting eastern G e r m a n y , i n par- ticular.
Data Appendix
A l l data are taken from Vierteljahrliche Volkswirtschaftliche Ge- samtrechnung des Deutschen Instituts fur Wirtschaftsforschung (DIW), Berlin, except
- the n o m i n a l interest rate, w h i c h is the " U m l a u f r e n d i t e festverzins- licher Wertpapiere" (Monatsberichte der Deutschen Bundesbank, various issues),
- the capital stock, w h i c h is due to L i i d e k e [Liideke et a l . , 1989, p . 11].
- the user cost o f c a p i t a l , w h i c h were calculated according to Jerger [1993, p p . 197f.] using input series k i n d l y p r o v i d e d b y L i i d e k e .
T h e capital stock is b r o a d l y defined, encompassing capital goods purchased by b o t h the private a n d the p u b l i c sector. A c c o r d i n g l y , the user cost o f c a p i t a l is calculated so as to cover the b r o a d aggregate o f gross fixed investment, t a k i n g into account the different real prices a n d depreciation rates o f different investment categories.
I n the measures o f >>—n and k—n (estimates o f (3') a n d (17)) y refers to (the l o g of) gross national p r o d u c t a n d n to hours w o r k e d , respectively.
T h e wage share (tVN/Y) (estimates o f (4') a n d (17)) is adjusted for changes i n the share o f self employment (base p e r i o d 1960:1) i n the usual manner. See, for example, Sachverstandigenrat [1992, p. 261].
O u t p u t at n o r m a l capacity u t i l i z a t i o n , Y*9 has been calculated according to Sachverstandigenrat [1992, p . 259].
The seasonal adjustment has been done w i t h E Z - X 1 1 , Version 2.00 o f Doan Associates, E v a n s t o n , I L ( U S A ) , w h i c h is a version o f Census X - l 1 o f the US Bureau of Census.
References
Bean, Charles, "Capital Shortages and Persistent Unemployment". Economic Policy, Vol. 8, 1989, pp. 12-53.
Bischoff, Charles, "The Effect of Alternative Lag Distributions". In: G . Fromm (Ed.), Tax Incentives and Capital Spending. Washington, D . C . , 1971, pp. 61-125.
Blanchard, Olivier, "Unemployment: Getting the Questions Right - and Some of the Answers". In: J. Dreze, C h . Bean (Eds.), Europe's Unemployment Problem. Cam- bridge, Mass., 1990, pp. 66-89.
-Stanley Fischer, Lectures on Macroeconomics. Cambridge, Mass., 1989.
Bruno, Michael, "Aggregate Supply and Demand Factors in O E C D Unemployment:
A n Update". Economica, Vol. 53, Supplement, 1986, pp. 35-52.
Jeffrey Sachs, The Economics of Worldwide Stagflation. Cambridge, Mass., 1985.
Burda, Michael, "Is There a Capital Shortage in Europe?". Weltmrtschaftliches Archiv, Vol. 124, 1988, pp. 38-57.
Clark, Peter, "Investment in the 1970s: Theory, Performance, and Prediction". Brook- ings Papers on Economic Activity, Vol. 1, 1979, pp. 73-113.
Corker, Robert, Owen Evans, Lloyd Kenward, "Tax Policy and Business Investment in the United States: Evidence from the 1980s". IMF Staff Papers, Vol. 36, 1989, pp. 31-62.
iMckey, David, Wayne Fuller, "Distribution of the Estimators for Autoregressive Time Series With a Unit Root". Journal of the American Statistical Association, Vol. 74, 1979, pp. 427-431.
"The Likelihood Ratio Statistic for Autoregressive Time Series With a Unit Root". Econometrica, Vol.49, 1981, pp. 1057-1072.
Dreze, Jacques, Charles Bean (Eds.) [1990a], Europe's Unemployment Problem, Cam- bridge, Mass., 1990.
- - [1990b], "Europe's Unemployment Problem: Introduction and Synthesis". In: J.
Dreze and C h . Bean (Eds.), Europe's Unemployment Problem. Cambridge, Mass., 1990, pp. 1-65.
Engle, Robert, Clive Granger, "Co-Integration and Error Correction: Representation, Estimation, and Testing". Econometrica, Vol. 55, 1987, pp. 251-276.
Entorf, Horst, Wolfgang Franz, Heinz Konig, Werner Smolny, "The Development of German Employment and Unemployment: Estimation and Simulation of a Small Macro Model". In: J. Dreze, C h . Bean (Eds.), Europe's Unemployment Problem.
Cambridge, Mass., 1990, pp. 239-287.
Fitoussi, Jean-Paul, Edmund Phelps, The Slump in Europe. Oxford, 1988.
Franz, Wolfgang, "Hysteresis, Persistence, and the N A I R U : A n Empirical Analysis for the Federal Republic of Germany". In: R. Layard, L . Calmfors (Eds.), The Fight Against Unemployment. Cambridge, 1987, pp. 91-122.
Gordon, Robert, "Back to the Future: European Unemployment Today Viewed from America in 1939". Brookings Papers on Economic Activity, Vol. 1,1988, pp. 271-304.
Hellwig, Martin, Manfred Neumann, "Economic Policy in Germany: Was There a Turnaround?". Economic Policy, Vol. 5, 1987, pp. 105-145.
Jerger, Jurgen, Beschdftigung und Kapitalbildung. Freiburg, 1993.
Kmenta, Jan, " A n Estimation of the C E S Production Function". International Eco- nomic Review, Vol. 8, 1967, pp. 180-189.
Krugman, Paul, "Slow Growth in Europe: Conceptual Issues". In: R. Lawrence, Ch.
Schultze (Eds.), Barriers to European Growth. Washington, D . C . , 1987, pp. 48-76.
Landmann, Oliver, Jurgen Jerger, "Domestic and Foreign Shocks to Employment and Capital Accumulation in Germany". In: H . Frisch, A . Worgotter (Eds.), Open-Econ- omy Macroeconomics. Houndmills, 1993, pp. 186-202.
Lawrence, Robert, Charles Schultze (Eds.), Barriers to European Growth. Washington, D . C . , 1987.
Layard, Richard, Charles Bean, "Why Does Unemployment Persist?". The Scandina- vian Journal of Economics, Vol. 91, 1989, pp. 371 -396.
Lindbeck, Assar, "Macroeconomic Theory and the Labor Market". European Eco- nomic Review, Vol. 36, 1992, pp. 209-235.
Liideke, Dietrich, Wolfgang Hummel, Thomas Rudel, Das Freiburger Modell. Heidel- berg, 1989.
Maddala, G.S., Econometrics. New York, 1977.
McCallum, John, "Wage Gaps, Factor Shares and Real Wages". The Scandinavian Journal of Economics, Vol. 87, 1985, pp. 436-459.
O E C D , Economic Surveys - Germany; 1987/88. Paris, 1988.
Paque, Karl-Heinz, Unemployment in West Germany - A Survey of Explanations and Policy Options. K i e l Working Paper, N o . 407. K i e l , 1990.
Phillips, Peter, "Understanding Spurious Regressions in Econometrics". Journal of Econometrics, Vol. 33, 1986, pp. 311-340.
- , "Time Series Regressions With A Unit Root". Econometrica, Vol. 55,1987, pp. 277- 301.
Pierre Perron, "Testing for a Unit Root in Time Series Regressions". Biometrika, Vol. 75, 1988, pp. 335-346.
Sachs, Jeffrey, "Real Wages and Unemployment in the O E C D Countries". Brookings Papers on Economic Activity, Vol. 1, 1983, pp. 255-289.
Sachverstandigenrat zur Begutachtung der gesamtwirtschaftlichen Entwicklung, Fur Wachstumsorientierung - Gegen lahmenden Verteilungsstreit. Stuttgart, 1992.
Sargan, J. Denis, Alok Bhargava, "Testing Residuals from Least Squares Regressions for Being Generated by the Gaussian Random Walk". Econometrica, Vol. 51, 1983, pp. 153-174.
Schultze, Charles, "Real Wages, Real Wage Aspirations, and Unemployment in Europe". In: R . Lawrence, C h . Schultze (Eds.), Barriers to European Growth. Wash- ington, D . C . , 1987, pp. 230-302.
Stock, James, "Asymptotic Properties of Least Squares Estimators of Co-Integrating Vectors". Econometrica, Vol. 55, 1987, pp. 1035-1056.
- , Mark Watson, "Testing for Common Trends". Journal of the American Statistical Association, Vol. 83, 1988, pp. 1097-1107.
