in Greece: A Multivariate Analysis of
Cointegrating Relationships
Georgios P. Kouretas, Department of Economics,
University of Crete
Leonidas P. Zarangas, Ministry of Labour, and Centre of Planning and Economic Research
This paper considers a nine-dimensional vector that is defined in accordance with a model of wage setting and demand for labor specified in a bargaining framework. The FIML multivariate cointegration technique is applied. Recent developments associated with this procedure are considered. First, a formal test developed by Paruolo (1996) for the presence of I(2) components in a multivariate context is applied along with the estimation of the roots of the companion matrix (Juselius, 1995). Second, structural restrictions identi-fying the long-run relations of interest are specified as proposed by Johansen and Juselius (1994) and Johansen (1995b), because more than one cointegrating vector is found. Restric-tions that characterize wage-setting and labor-demand schedules are imposed and tested, first separately and then jointly. Finally, stability tests proposed by Hansen and Johansen (1993) are applied, and it is shown that the dimension of the cointegration space is sample independent and the estimated coefficients do not exhibit instability in recursive estimations. 2000 Society for Policy Modeling. Published by Elsevier Science Inc.
Key Words: Cointegration;I(2) Analysis; Companion matrix; Identification; Stability; Wage determination; Labor demand.
Address correspondence to Dr. Georgios P. Kouretas, 40 Argonafton Street, GR-15125, Maroussi, Greece.email: [email protected]
An earlier version of this paper was presented at the 1996 Annual Conference of the European Association of Labour Economists, held in Chania, Greece, 19–22 September 1996. Thanks are due to conference participants for many valuable comments. We also thank George Alogoskoufis, Vassilis Droukopoulos, Dimitris Georgoutsos, Dimitris Moschos, Yan-nis Stournaras, and Timo Tyrvainen for many helpful comments and discussions. We also thank an anonymous referee for his constructive comments. The usual disclaimer applies.
Received September 1996; final draft accepted February 1997.
Journal of Policy Modeling22(2):171–195 (2000)
172 G. P. Kouretas and L. P. Zarangas
1. INTRODUCTION
During the last decade econometrics of nonstationary variables has undergone a great deal of development, having as a starting point the seminal paper of Engle and Granger (1987), which intro-duced the concept of cointegration and its relevance in investigat-ing the existence of long-run relationships that are suggested by economic theory. Within the subject of labor economics, the issues of wage determination and labor demand are often candidates for testing such kinds of long-run relations, and the relevant litera-ture is therefore substantial.
In the present paper, wage setting and demand for labor in Greece are investigated, applying the Johansen FIML multivariate cointegration methodology. In addition, we apply several recent developments that are associated with this approach. First, a for-mal test developed by Paruolo (1996) is used to test for the pres-ence ofI(2) components in the multivariate framework. This test is coupled with the roots of the companion matrix as suggested by Juselius (1995), and we are thus able to identify the order of the system and the dimension of the cointegration space in a more precise way. Second, we pay particular attention to issues related to identification of the system by imposing linear and homogeneous restrictions as suggested by Johansen and Juselius (1994) and Johansen (1995b). Finally, three tests of parameter stability in VAR models proposed by Hansen and Johansen (1993) are ap-plied to examine whether the rank of the cointegration space is sample independent, and if the estimated coefficients are stable in recursive estimations. Therefore, we are interested in: (1) formal identification, which is related to the statistical model; (2) empirical identification, which is related to the actual estimated parameters; and (3) economic identification, which is related to the economic interpretability of the estimated coefficients of a formally and empirically identified model.
2. THE ECONOMIC MODEL
There are n identical firms, which have a production function Q5F(N,m,K,t) with three inputs: labor (N); raw materials (m); and capital (K), which is treated as predetermined. Technical progress (steady) is embodied in t. Imperfect competition is as-sumed to prevail in the product market. The first maximizes profits, which are defined as the difference between sales revenues and production costs (Eq. 1):
p 5Pˆ[Z˜ F(N,m,K)]F(N,m,K)2W(11s)N2Pmm (1)
whereQˆd5pˆ21(P)Z˜21;D(P)Zis a downward sloping demand curve of the separable form introduced by Nickell (1978). Here, Z 5 Z˜21 is a parameter describing the position of the demand
curve faced by the firm and Pˆ is the producer price of the firm that is considered endogenous,P5competitors’ producer price, W5nominal consumer wage,s5payroll tax,Pm5price of raw materials (including energy). The output of the firm,Q, is treated as endogenous. According to the marginal product condition, opti-mal use of an input is determined by the relative price. If the firm uses raw materials optimally, the demand for labor schedule has the following standard form (Eq. 2):
Nd5Nd
1
W(11s) P ,Z,Pm
P,K,t
2
(2)In an organized labor market the firm bargains with a union. The welfare of the union depends on the after-tax real wage of its employed members and the (real) unemployment benefit received by the unemployed members,U5U(W(12 t)/Pc,N,B), wherePc is the consumer prices, t is the income taxes, andB is the replacement ratio (unemployment benefit in real terms). The partial derivatives of this general preference function are:
U91,U92,U93.0 andU″1,U″2,U″3,0.
The union model that is used in this paper is a “right-to-manage” model that assumes that wages are bargained over and the profit-maximizing firm sets employment unilaterally. The game is speci-fied as a standard Nash solution of a cooperative game following Binmore and colleagues (1986) (Eq. 3):
max w
(U2U0)u(p 2 p0)12us.t.N(.)5arg N
174 G. P. Kouretas and L. P. Zarangas
whereurefers to the bargaining power of unions, 0, u , 1. U0
is the fall-back utility of the union in the event that an agreement is not reached. In Greece, the relevant alternative to an agreement is a strike. Thus, we assume that theU0depends on strike
allow-ances,U05U0(A).p0is the fall-back profit that reflects fixed costs
during a production stoppage. When p0 is deducted from the
“undercontract” profits, fixed costs cancel out. For simplicity fixed costs were already omitted from Equation 1.
The model for the equilibrium (real) wage consists of variables influencing profits, on the one hand, and the utility of the union, on the other hand. In addition, a role is played by determinants of the fall-back utilities of the parties. Finally, relative bargaining power is important. The general form of the wage-setting schedule is (Eq. 4):
W*5W(P,s,t,Pc
P,u,Pm,Z,B,A,K,t) (4)
Indirect tax,yexerts an influence as part of the price wedge, Pc/P.
3. ECONOMETRIC METHODOLOGY
A visual examination of the data reveals that the observations are strongly time dependent, pointing to the need for models based on adjustment to steady states. Given the definitions of theZit series in Section 4 below, it would be hard to accept the assumption that any of them could be nonstochastic. Therefore, a probability formulation of the whole data is needed.
A formal framework was suggested by Hendry and Richard (1983), where the joint probability function for the data was given in the form of sequential probabilities conditional on past values of the process. By allowing for a set of conditioning variablesDt5
[d1t, . . . , dqt] to control for institutional factors, and assuming multivariate normality, the vector autoregressive model is ob-tained as a tentative statistical model for the data-generating pro-cess. In the error correction term it is given by (Eq. 5):
Dzt5 G1Dzt211. . .1 Gk21Dzt2k111 Pzt2k1 gDt1 m 1 et (5) whereet|Niidp(0,S). The parameters (G1, . . . ,Gk21,g) define the
probably crucial for a successful estimation of the steady-state relations of interest.
Model (5) will be treated as the benchmark model, within which all the subsequent hypotheses are tested. Because the parameter set u 5 (G, . . . , Gk21,P,g,m,S) varies unrestrictedly, it follows
that the I(1) and the I(2) models are submodels of (5). In the unrestricted form, therefore, model (5) corresponds to the I(0) model. Hence, in the statistical sense theI(0) model is the most general, because the higher order models are nested in this model. For simplicity we assume k 52 in all subsequent discussions of model (5), i.e. (Eq. 6),
Dzt5 G1Dzt211 ab9zt221 gDt1 m 1 et (6)
3A. The I(1) Model
Johansen (1991) shows that ifZi|I(1), the following restrictions on model (6) have to be satisfied (Eq. 7):
P 5 ab9, (7)
wherePhas reduced rank,r, a, andbare (p3r) matrices, and (Eq. 8)
C 5 a⊥(2I1 G1)b⊥5 wh9, (8)
whereCis a (p-r)3(p-r) matrix of full rank,wandhare (p-r)3
(p-r) matrices, and a⊥and b⊥are p3 (p-r) matrices orthogonal to a and b, respectively. The parameterization in (7) and (8) facilitates the investigation of, on the one hand, the r linearly independent stationary relations between the levels of the vari-ables and, on the other hand, the p 2 r linearly independent nonstationary relations. This duality between the stationary rela-tions and the nonstationary common trends is very useful for a full understanding of the generating mechanisms behind the cho-sen data. Although the autoregressive (AR) reprecho-sentation of the model is useful for the analysis of the long-run relations in the data, the moving average (MA) representation is useful for the analysis of the common stochastic and deterministic trends that have generated the data.
3B. TheI(2) Model
If condition (8) for theI(1) model is violated, the processZtis integrated of second order or higher. When the process isI(2), it is useful to rewrite model (6) in second differences (Eq. 9):
D2zt
176 G. P. Kouretas and L. P. Zarangas
whereG 5 2I1 G1and ab9has reduced rankr. IfZt|I(2), the
following restriction on the parameters of model (9) has to be satisfied (Eq. 10):
C 5 a9⊥Gb⊥5 wh, (10)
wherewand h are (p-r) 3s1matrices and s1, (p 2r).
Johansen (1997) shows that the space spanned by the vectorZt can be decomposed into r stationary directions, b, and p 2 r nonstationary directions, b⊥, and the latter into the directions (b1
⊥,b2⊥), where b1⊥5 b⊥h is of dimension p 3 s1 and b2⊥ 5 b⊥(b9⊥b⊥)21h
⊥ is of dimesnion p 3 s2 and s1 1 s2 5 p-r. The
properties of the process are described by
I(2):hb2
where v is a p 3r matrix of weights, designed to pick out the I(2) components of Zt(Johansen, 1995a).
Johansen (1991) shows how the model can be written in moving average form, while Johansen (1997) derives the FIML solution to the estimation problem for theI(2) model. Furthermore, Johansen (1995a) provides an asymptotically equivalent two-step procedure that is computationally simpler. It applies the standard eigenvalue procedure derived for the I(1) model twice: first to estimate the reduced rank of thePmatrix, and then, for given estimates ofa
andb, to estimate the reduced rank ofaˆ9⊥Gbˆ⊥(Juselius 1994, 1995, 1996, provides a complete statistical analysis).
3C. The Identification Problem
In a multivariate framework like the one provided by the wage model under consideration, a vector error correction model may contain multiple cointegrating vectors. In such a case the individual cointegrating vectors are underidentified in the absence of suffi-cient linear restrictions on each vector. Recently, Johansen and Juselius (1994) and Johansen (1995b) have addressed the issue of identification in cointegrated systems.
of each of the r cointegrating vectors is that we can impose at leastr21, just identifying restrictions and one normalization on each vector, without changing the likelihood function. This is a necessary condition. The necessary and sufficient condition for identification of theith cointegration vector, the Rank condition, is that the rank (b9Hi)5r21, whereHiis the design (or restric-tion) matrix for the corresponding ith cointegrating vector. Jo-hansen and Juselius (1994) provide a likelihood ratio statistic to test for overidentifying restrictions that is distributed asx2 with
v5 Si(pl2r112si) degrees of freedom, whereplis the number of freely estimated parameters inbi.
3D. Parameter Stability in Cointegrated VAR Models
An equally important issue along with the existence of at least one cointegration vector is the issue of stability of such relation-ships through time as well as the stability of the estimated coeffi-cients of such relationships. Thus, Sephton and Larsen (1991) have shown that Johansen’s test may be characterized by sample dependency.
Hansen and Johansen (1993) have suggested methods for the evaluation of parameter constancy in cointegrated VAR models, formally using estimates obtained from the Johansen FIML tech-nique. Three tests have been constructed under the two VAR representations of Equation 6. In the “Z-representation” all the parameters of model (6) are reestimated during the recursions, while under the “R-representation” the short-run parametersGi, i51 . . .k, are fixed to their full sample values and only the long-run parameters in Equation 6 are reestimated.
178 G. P. Kouretas and L. P. Zarangas
A second test deals with the null hypothesis of constancy of the cointegration space for a given cointegration rank. Hansen and Johansen propose a likelihood ratio test that is constructed by comparing the likelihood function from each recursive subsample with the likelihood function computed under the restriction that the cointegrating vector estimated from the full sample falls within the space spanned by the estimated vectors of each individual sample. The test statistic is ax2distributed with (p-r)rdegrees of
freedom.
The third test examines the constancy of the elements of the cointegrating vectors. When more than one cointegration vector is identified, then it is unclear which are the parameters whose time path should be plotted. The proposed test exploits the fact that there is a unique relationship between the eigenvalues and the estimated eigenvectors, given the normalization from which they have been obtained. Hansen and Johansen (1993) have de-rived the asymptotic distribution of the eigenvalues, which allows us to plot the estimated eigenvalues along with their confidence bounds. This allows us to test whether the eigenvalue at the partic-ular date differs significantly from its full sample value. The ab-sence of any particular trend or shift in the plotted values of the estimated eigenvalues is considered to be an indication in favor of the constancy of the cointegrating vectors.
4. THE EMPIRICAL VECTOR AUTOREGRESSIVE MODEL 4A. The Data
The basic variables inztsuggested by the discussion in Section 3 are:
W5nominal wages P5producer prices N5employment
Q5output volume, which enters as a proxy for the demand shift factor,Z l2 ta5average income tax rate
11s5rate of employers’ social security contributions
CPI/P5the price wedge, i.e., the consumer price relative to the producer price, which also proxies the effect of the indirect tax,y
Pm5price of imported raw materials (including energy)
UNION5unionization rate, which is a proxy for the bargaining power of the unions.
Monthly Bulletin of the Bank of Greece and some from the Minis-try of Labour data bank. Furthermore, it has been shown that there is a major difference between the behavior of the wage and employment series for the public sector and the rest of the economy. We, therefore, exclude the public sector and focus on the analysis of the private sector. Moreover, because our main interest is the study of real wage resistance, i.e., the impact of taxes on wage setting and demand for labor, we omit variables of great interest such as the capital stock and the related user cost as well as unemployment benefits and strike allowances (Tyr-vainen, 1992, 1995; Lockwood and Manning, 1993). This is neces-sary to make our system manageable. Finally, we use a vector of dummiesDtthat includes three centered seasonal dummies that account for the short-run effects that will otherwise violate the Gaussian assumption about the residuals, and we use two interven-tion dummies as well. The first one captures the change in political regime, and takes the value zero for the period 1974–81, when the conservative party was in power, and 1 for the period 1981 to 1989 when the socialist party was in power. The second policy dummy variable reflects the effects of political cycles and takes the value of 1 during election years and zero otherwise.
4B. Testing the General Specification of the Model
All empirical models are inherently approximations of the ac-tual data generating process, and the question is whether the benchmark model (6) is a satisfactorily close approximation. Two different aspects of the model will be investigated: (1) the stochas-tic specification regarding residual correlation, heteroscedasstochas-ticity, and normality; and (2) the relevance of the conditioning variables inDt. These two aspects of the model are clearly related in the sense that residual misspecification often arises as a consequence of omitting important variables inDt.
According to the residual tests reported in Table 1, the bench-mark model fork53 andztand Dtas specified above, seems to provide a reasonably good approximation of the data-generating process. The estimated residual standard deviations are generally very small, indicating that most of the variation of the vector process can be accounted for by the chosen information set.
180
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Table 1: Residual Misspecification Tests of Model (6) with k53
Eq. se h1(21) h2(2) Skew. Ex.kurt. h3(2)
Dlw 0.017 35.0 1.7 0.05 3.09 0.73
Dlp 0.013 13.9 1.3 0.64 5.08 10.96
Dln 0.009 25.4 0.9 0.72 3.30 7.43
Dlq 0.019 29.9 1.2 0.07 2.42 0.53
Dl(12ta) 0.004 17.3 0.0 0.52 5.91 19.69
Dl(11s) 0.001 23.5 0.8 1.17 6.57 14.74
Dl(CPI/P) 0.009 27.6 2.5 20.49 3.08 3.10
Dlpm 0.011 30.0 1.1 0.01 3.28 1.60
Dlunion 0.014 19.8 2.6 20.26 7.80 45.01
Relevance of the Conditioning Variables in the VectorDt
Eq. Dw Dp DN DQ D(12ta) D(11s) DCPI/P DPm DUNION
D1 0.0111 0.0011 0 0.0051 0.0182 0 0 0 0.0231
D2 0.0431 0.0152 0.0031 0 0.0222 0 0 0 0
h1(v) is the Ljung-Box test statistic for residual autocorrelation,h2(v) is the ARCH test for heteroscedastic residuals, andh3(v) the Jarque-Bera test for normality. All test statistics are distributed asx2withvdegrees of freedom.
Table 2: Testing the Rank in thel(2) and thel(1) Model
Testing the joint hypothesisH(s1>r)
p-r r Q(s1>r)H0
9 0 625.9 497.4 435.6 389.4 355.5 324.6 298.3 276.8 246.9
502.9 454.8 411.2 372.1 332.9 299.5 269.8 243.9 221.9
8 1 456.9 404.3 365.6 304.5 287.8 249.1 234.2 199.2
405.1 363.4 324.1 287.4 256.1 227.4 203.3 183.2
7 2 344.3 303.4 267.9 240.9 201.3 188.2 175.6
317.5 280.2 245.5 215.5 188.4 166.1 147.5
6 3 277.2 235.8 195.0 166.8 143.2 125.9
240.3 206.8 179.0 154.1 132.8 115.4
5 4 226.6 189.7 155.4 122.7 114.3
171.9 145.6 122.0 102.7 86.9
4 5 154.3 124.5 99.5 84.3
116.3 94.7 76.8 63.1
3 6 100.6 87.5 67.8
70.8 54.5 42.9
2 7 68.5 29.2
36.1 26.0
1 8 19.2
12.9
s2 9 8 7 6 5 4 3 2 1
The numbers in italics are the critical values (Paruolo, 1996; Table 5).
expected, both intervention dummies that refer to change in politi-cal regimes and to politipoliti-cal cycles have their significant effect mainly on the wage rate, the price level, and the tax rate, and a lesser effect on employment and output.
4C. Determining the Cointegration Rank and the Order of Integration
The two-step procedure analyzed in Johansen (1995a) is used to determine the order of integration in a multivariate context and the rank of the necessary matrices. The hypothesis that the number ofL(1) trends5s1and the rank5ris tested against the unrestricted
H0model based on a likelihood ratio test procedure discussed in
Paruolo (1996a). The test statistics reported in Table 2 have been calculated for all values of r and s91 5 p 2 r 2 s2, under the
assumption that the data contain linear but no quadratic trends.1
Table 2 presents the results of the formal tests for the presence of I(2) components in the multivariate context. The 95 percent
182 G. P. Kouretas and L. P. Zarangas
quantiles of the asymptotic test distributions are taken from Table 5 Paruolo (1996), and reproduced underneath the calculated test val-ues. Starting from the most restricted hypothesis {r50,s150, and
s259} and testing successively less and less restricted hypotheses
according to the Pantula (1989) principle shows that essentially all I(2) hypotheses can be rejected on the 5 percent level.
In addition to the formal tests, Juselius (1995) offers further insight into the I(2) and I(1) analysis and the determination of the correct cointegration rank. She argues that the results of the trace and maximum eigenvalue test statistics of the I(1) analysis should be interpreted with some caution: First, the conditioning on intervention dummies and weakly exogenous variables is likely to change the asymptotic distributions to some (unknown) extent. Second, the asymptotic critical values may not be very close ap-proximations in small samples. Juselius (1995) suggests the use of the companion matrix as an additional tool for determining the correct cointegration rank.
The roots of the companion matrix are calculated from the estimation of the model without allowing forI(2) trends, i.e., we estimate the standardI(1) model. This estimation shows that the first six unit roots are very close to unity, ranging from 0.99 to 0.91, while the next three are well inside the unit circle, ranging from 0.75 to 0.45. This result seems to support the choice of six unit roots in the time series process and three long-run relation-ships, and it is in line with the results of the formal test of I(2) components. The estimated roots are shown in Figure 1.
Table 3 reports the results of the Johansen-JuseliusI(1) cointe-gration analysis.2,3 We have included in the estimation procedure
three centered seasonal dummies and two shift dummies, which account for the change in political regime and for the effects of political cycles. To take into consideration the two issues raised by Juselius (1995) we have simulated the critical values for the trace test using the DisCo routine developed by Johansen and Nielsen (1993), and we have made a small sample adjustment to these statistics according to Reimers (1992). Both the trace and maximum
2The calculations of the eigenvectors as well as the stability tests have been performed using the program CATS in RATS 4.20 developed by Henrik Hansen and Katarina Juselius (1995), Estima, IL.
3A small sample adjustment has been made in all likelihood ratio statistics equal to
22lnQ5 2(T2kp) o k
i5r011
ln(12 l),
Figure 1. The eigenvalues of the companion matrix.
eigenvalue statistics reject the existence of zero cointegrating vectors or nine common trends. The two statistics suggest that we can accept three significant cointegrating vectors. These results reconfirm the decision made based on the roots of the companion matrix.
Table 3 also reports the results of several significant tests. Ac-cording to the first test, none of the variables of the system is nonrelevant and, hence, could be excluded from the cointegrating vector (the exclusion test). The second test shows that all series are in a nonstationary conditional upon three cointegration vectors (the multivariate stationarity test). Finally, weak exogeneity is tested with the last test, and it is rejected for all variables of our system. In addition, Table 3 reports the multivariate residual statistics, because the Gaussian assumption is violated in the pres-ence of nonnormality, serial correlation, and conditional hetero-skedasticity in the residuals of the VAR. No evidence of serious misspecification was detected.4
184 G. P. Kouretas and L. P. Zarangas
Table 3: Johansen-Juselius cointegration tests
95 Percent critical values
r Trace lmax Trace lmax
r50 312.411 78.031 223.35 66.89
r<1 234.391 64.341 168.98 60.34
r<2 170.051 50.141 135.78 49.12
r<3 99.87 38.59 100.60 42.33
r<4 81.31 29.75 84.98 37.45
r<5 51.57 22.26 60.09 33.88
r<6 29.31 18.01 33.43 31.56
r<7 11.30 9.75 14.67 12.56
r<8 1.55 1.55 3.45 3.45
Exclusion Stationary Weak
Variable restrictions test exogeneity
lw 9.811 26.401 9.731
lp 25.211 25.961 10.081
ln 8.441 29.081 9.721
lq 21.931 20.981 8.221
l(12 ta) 9.651 28.221 9.051
l(11s) 8.201 32.901 10.021
l(CPI/P) 10.341 30.551 8.931
lpm 32.011 25.531 14.381
lunion 17.011 26.081 14.901
Multivariate residual statistics
LB(17)51461.63(0.06) x2(18)568.98(0.02)
Notes: rdenotes the number of eigenvectors. Trace andlmax denote, respectively, the trace and maximum eigenvalue likelihood ratio statistics. The 95-percent critical values have been simulated using the Johansen-Nielsen (1993) DisCo program for a model with two intervention dummies. In performing the Johansen-Juselius tests, a structure of three lags was chosen according to a likelihood ratio test, corrected for the degrees of freedom and the Ljung-Box Q statistic for detecting serial correlation in the residuals of the equations of the VAR. A model with an unrestricted constant in the VAR equation is estimated according to the Johansen (1992) testing methodology.
1Indicates statistical significance at the 5 percent critical level.
Notes:For the test of exclusion restrictions figures arex2statistics with three degrees of freedom, for the stationarity test figures arex2with five degrees of freedom, and for the weak exogeneity test figures arex2with three degrees of freedom.
Figure 2. The Trace tests.
Figures 2–4 report the results of applying the recursive tests for parameter stability of Johansen’s results. Figure 2 shows that the rank of the cointegration space does not depend on the sample size from which it has been estimated, because we are unable to reject the null hypothesis of a constant rank—in our case three accepted eigenvectors. Furthermore, Figure 3 shows that we al-ways accept the null hypothesis of the constancy of the cointegra-tion space for a given cointegracointegra-tion rank. Finally, Figure 4 shows that the estimated coefficients do not exhibit instability in recursive estimation, because each corresponding eigenvalue has no signifi-cant trend or shift during the period under investigation.
4D. Structural Identification
186 G. P. Kouretas and L. P. Zarangas
Figure 3. Test of known beta eq. to beta(t).
impose independent linear restrictions based on structural hypoth-eses implied by economic theory so that we assign each vector to a specific structure. Given that we have three significant vectors, it is expected that one will be the wage-setting equation, the second the demand for labor, and the third can take alternative economic structures. Below, these restrictions are made explicit. We first consider the following relationship:
logW5 bPlogP1 bNlogN1 bQlogQ
1 btalog(12 ta)1 bslog(11s)1 bylog(CPI/P)
1 bPmlog(Pm)1 bUlog(UNION) (11)
For this relation to be considered as a wage-setting schedule the signs should be:
bP>0,bQ>0,bta<0,bs<0,by>0,bU>0, and possiblybPm<0.
Figure 4. Test for the eigenvalues.
the dominant role. In the second the firms are the dominant player. These hypotheses also indicate how taxes and relative prices enter the wage equation. There are several alternative restrictions that we may impose on the wage relation. One possibility is that we assume wage resistance; then we could impose a wedge-restriction like:
2bta5 by511 bs5 v (12)
in Equation 11, which is a standard way to proceed when no distinction is made between proportional and marginal income tax rates. Ifv 51, the taxes fall fully on the firm. Ifv 50, they fall fully on the worker. In Table 4 we give the full set of restrictions imposed on the wage equation.
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Table 4: FIML Estimated Coefficients and Identification
Wage setting Labor demand Output
Coeff. Variables bi ai bi ai bi ai
bw W 1.000 0.003 20.163 20.100 1.260 20.008
bP P 21.616 0.022 0.523 20.014 21.912 20.002
bN N 1.045 0.015 1.000 20.012 20.414 0.018
bQ Q 21.955 0.041 21.142 0.125 1.000 0.009
bta 12 ta 2.283 20.007 20.032 20.004 22.854 0.005
bs 11s 2.840 20.001 25.401 0.009 1.640 0.001
by CPI/P 22.704 20.011 20.338 0.045 2.300 20.009
bPm Pm 2.007 20.036 20.506 0.033 1.153 20.001
bU UNION 20.116 20.064 0.063 21.267 0.011 20.259
Hypothesis testing
Wage setting Labor demand Output
(1) (2) (3) (4) (5)
bw5 2bP5 bw5 2bP bw5 2bP bw5 2bP5 bw5 2bP5
2bPm5 bta, 2bPm5 bN5 2bPm5 bs, bs, bta5 2by,
bN5 2bQ, 2bQ5 2bta, bta5 bye5 bta5 by5 bN5 2bQ,
bta512bs5 bta512bs5 bU50 bPm5 bU50 bs5 bPm5
2by 2by bU50
x251.03 x255.03 x257.33 x253.99 x255.78
Q(16)511.59 Q(16)510.45
SETTING,
TAXES,
AND
LABOR
IN
GREECE
189
Table 4: Continued
Estimates of the impact of cumulated innovations in variablej, on variablek
k/j w P N Q 12ta 11s CPI/P Pm UNION
w 20.082 20.610 0.171 0.129 20.958 4.049 0.300 20.2 0.018
P 0.021 0.477 0.176 0.142 0.035 0.604 0.202 0.4 0.008
N 20.009 0.230 0.431 20.135 0.405 20.379 0.803 20.1 0.001
Q 20.011 20.041 20.006 0.177 0.236 0.707 0.176 0.04 0.009
12 ta 0.012 20.100 0.073 0.079 20.171 20.352 0.002 0.1 0.002
11s 0.011 0.006 0.014 20.005 0.017 0.113 0.038 20.0 0.000
CPI/P 0.035 20.111 0.381 0.162 20.254 21.335 0.331 0.2 0.006
Pm 20.015 0.592 0.089 0.289 0.152 21.101 20.073 0.7 0.009
UNION 0.584 25.291 23.975 7.262 23.659 17.710 25.972 4.2 0.243
Notes:All tests arex2distributed with 5, 6, 6, and 8 degrees of freedom respectively. Q(.) is the Johansen and Juselius (1994) test for overidentifying restrictions and is ax2distributed with 16 degrees of freedom.
190 G. P. Kouretas and L. P. Zarangas
the expected signs of the coefficients should be bw< 0, bP > 0,
bQ>0,bta50,bs<0,by50, and possiblybPm< 0. The impacts of both the income tax and the indirect tax derive from their wage effect. If the union has a direct influence on employment (for a given wage), thenby?0. The restrictionbw5 2bP5 2bQ5 bs.0 implies that it is the real labor cost for a produced unit that is important. Again, if it is the relative raw material price that is important, we writebw5 2 bP 2 bPm2 bQ5 bs.
We concluded above that there are probably three cointegrating vectors in our data space. Two of them are well specified, i.e., a wage-setting schedule and demand-for-labor condition. The third eigenvector could describe either the demand side or the supply side of the variables concerned. Thus, we expect the following to be possible candidates: (1) the supply of output, (2) the demand for output, (3) the constant mark-up pricing rule, and (4) price setting conducted by the product-market demand conditions. How-ever, the resulting “semirelations” may also be mixtures of two or more competing but misspecified relations. Hence, one should not put too much emphasis on the interpretation of the remaining vectors. Table 4 introduces the three nonrestricted eigenvectors. The strategy applied below is as follows. First, we do partial identification for each of the three vectors based on the wage setting, demand for labor and the other “semirelations.” This sort of identification is done through the imposition of linear and homoge-neous restrictions on each vector (Johansen and Juselius, 1990, 1992). Second, following Johansen and Juselius (1994) and Jo-hansen (1995a) and the discussion in Section 3C, we provide formal identification of the joint hypotheses of the complete model.
5. TESTING STRUCTURAL HYPOTHESES
representation of the model. As is shown the innovations from the price level, the level of employment and the output have the largest effect on the wage rate, while the effect of the degree of unionization is low.
We proceed by imposing restrictions describing long-run prop-erties that the vectors of interest are expected to fulfill. Short-term adjustment (to changes in the process and in the long-run steady states) is determined freely. However, insofar as relevant cointegrating relations with behavioral interpretation will be de-tected, we expect the error-correcting property to reveal them even more clearly.
5A. Wage-Setting Schedule
First, we evaluate the two extreme hypotheses concerning the dominance of the bargaining parties and the tax incidence aug-mented with the restriction (bN5 2bQ), which makes productivity the driving force of real wages. We are unable to reject both contradictory hypotheses. The hypothesis of union dominance (with taxes fully borne by firms) generates ax2statistic equal to
1.03, whereas the opposite hypothesis has ax2value of 5.09. Given
this outcome, we proceed to test whether the absolute values of the coefficients of (l2 ta), (l1s), (CPI/P) are equal in absolute
value. This restriction was also accepted. Furthermore, column 2 indicates that the long-run homogeneity hypothesis between the real wage and productivity is rejected, and this result may be attributed to the presence of a linear trend in the model. Finally, we impose the restriction for testing the degree of wage indexation that is given in Equation 12. In column 1 it is shown that this restriction for the case of real wage resistancev 51 is accepted and, therefore, it can be argued that the Greek labor market exhibits a considerable degree of real-wage resistance.
5B. Demand for Labor
The definition of the demand-for-labor schedule was given above. As is clear from Equation 2, the payroll tax is the only tax factor included. Therefore, we should expect thatbta 5 by5 0.
192 G. P. Kouretas and L. P. Zarangas
for labor is guided by real labor cost and the level of activity. However, the absolute values of elasticities with respect to both these factors are significantly below unity, which would be ex-pected under simple Cobb-Douglas technology.
Given these findings, it appears that there is some evidence against the efficient bargaining model. In the right-to-manage model (3) that we consider here, employment is determined by the profit-maximizing condition (2), which only includes variables entering the profit function. In the efficient bargaining model the profit maximization condition is relaxed and employment is defined in the bargaining solution. In this case, all variables enter-ing the game play a role in the determination of employment. Thus, the determinants of profit enter the employment function significantly while other variables do not. This indicates that the equilibrium level of employment is on the labor demand curve.
Column 4 indicates that the effect of real raw material prices does not differ significantly from zero. This finding leads to the same conclusion that holds in several countries, as Hamermesh (1991) has shown. He argues that labor and energy are price substitutes, with a very small crossprice elasticity, and thus it is not surprising that we were unable to distinguish an impact for raw material prices on the demand for labor function. Finally, we impose the restriction that the output elasticity is equal to the labor cost effect, and it is easily rejected.
5C. Output “Semischedule”
The cointegration results have shown that there is a third statisti-cally significant eigenvector. As we have explained, this vector can capture elements of both the demand side and the supply side of the labor market. In column 5 we consider one possibility, namely that the third vector resembles a demand-for-output sched-ule, and it is clear that we are unable to reject the required restric-tions. However, given that the hypothesis for the Cobb-Douglas technology, (bN 5 2bQ) is also accepted, this could also capture supply-side elements.
5D. Joint Hypotheses
Johansen and Juselius (1994), and the results are given in Table 4. Because there is a large number of combinations that we could make, we present here only the analysis of the full set of restric-tions. Thus, the first case is that we consider columns 1, 3, and 5, and the second one refers to columns 2, 4, and 5. In both cases it is shown that we pass the test for overidentifying restrictions, because the value of the likelihood ratio statisticQwith 16 degrees of freedom is equal to 11.59 and 10.45 in the first and second cases, respectively, and therefore, we argue that the system of the three statistically significant vectors resembles the three long-run relationships that we have considered, namely, the wage-setting schedule, the demand-for-labor schedule, and the output schedule.
6. CONCLUSIONS
194 G. P. Kouretas and L. P. Zarangas
the testing methodology suggested by Hansen and Johansen (1993) that the identified long-run relationships are sample inde-pendent, and that the estimated coefficients do not exhibit instabil-ities in recursive estimations.
The major findings of this paper lead to the conclusion that in the private sector in Greece, neither of the bargaining parties—employ-ers or employees—has gained full dominance in the wage-setting process. In addition parameter estimates indicate a considerable degree of real-wage resistance. Finally, equilibrium employment appears to be on the labor demand curve in the aggregate private sector in Greece, and this contradicts the efficient bargaining hy-pothesis (Layard, Nickell, and Jackman, 1991).
REFERENCES
Bean, C. (1992) European Unemployment: A Survey, London School of Economics. Centre for Economic Performance. Discussion Paper No 71.
Binmore, K., Rubinstein, A., and Wolinsky, A. (1986) The Nash Bargaining Solution in Economic Modelling.Rand Journal of Economics17:176–188.
Engle, R.F., and Granger, C.W.J. (1987) Co-Integration and Error Correction: Representa-tion, EstimaRepresenta-tion, and Testing.Econometrica55:251–276.
Gonzalo, J. (1994) Comparison of Five Alternative Methods of Estimating Long-Run Equilibrium Relationships.Journal of Econometrics60:203–233.
Harmermesh, D.S. (1991) Labor Demand: What Do We Know? What Don’t We Know? NBER Working Paper 3890.
Hansen, H., and Johansen, S. (1993)Recursive Estimation in Cointegrated VAR Models, Reprint 1. Copenhagen: Institute of Mathematical Statistics, University of Copen-hagen.
Hansen, H., and Juselius, K. (1995)CATS in RATS Manual to Cointegration Analysis of Time Series.Evanston, IL: Estima, Inc.
Hendry, D.F., and Richard, J.-F. (1983) The Econometric Analysis of Economic Time Series (with discussion).International Statistical Review51:111–163.
Johansen, S. (1991) Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models.Econometrica59:1551–1581.
Johansen, S. (1992) Determination of Cointegration Rank in the Presence of a Linear Trends.Oxford Bulletin of Economics and Statistics54:383–397.
Johansen, S. (1995a) A Statistical Analysis of Cointegration for I(2) Variables.Econometric Theory11:25–29.
Johansen, S. (1995b) Identifying Restrictions of Linear Equations.Journal of Econometrics
69:111–132.
Johansen, S. (1997) A Likelihood Analysis of the I(2) Model.Scandinavian Journal of Statistics24:433–462.
Johansen, S., and Juselius, K. (1992) Testing Structural Hypotheses in a Multivariate Cointegration Analysis of the PPP and UIP for UK. Journal of Econometrics
53:211–244.
Johansen, S., and Juselius, K. (1994) Identification of the Long-Run and the Short-Run Structure: An Application to the ISLM Model.Journal of Econometrics63:7–36. Johansen, S., and Nielsen, B. (1993) Asymptotics for Cointegration Rank Test in the
Presence of Intervention Dummies: Manual for the simulation program DisCo, Reprint. University of Copenhagen.
Juselius, K. (1994) On the Duality Between Long-Run Relations and Common Trends in theI(1) and the I(2) case: An Application to the Aggregate Money Holdings.
Econometric Reviews13:151–178.
Juselius, K. (1995) Do Purchasing Power Parity and Uncovered Interest Rate Parity Hold in the Long Run? An Example of Likelihood Inference in a Multivariate Time-Series Model.Journal of Econometrics69:211–240.
Juselius, K. (1996) A Structured VAR Under Changing Monetary Policy. Discussion Paper, Department of Economics, University of Copenhagen.
Layard, R., Nickell, S., and Jackman, R. (1991)Unemployment.Oxford: Oxford University Press.
Lee, T.-H., and Tse, Y. (1996) Cointegration Test With Conditional Heteroskedasticity.
Journal of Econometrics73:401–410.
Lockwood, B., and Manning, A. (1993) Wage Setting and the Tax System: Theory and Evidence for the UK. London School of Economics, Centre for Economic Perfor-mance, Discussion Paper 115.
Manning, A. (1992) Wage Bargaining and the Phillips Curve: The Identification and Specification of Aggregate Wage Equations. London School of Economics, Centre for Economic Performance, Discussion paper 62.
Nickell, S.J. (1978)The Investment Decisions of Firms.Cambridge: Cambridge University Press.
Pantula, S.G. (1989) Testing for Unit Roots in Time Series Data.Econometric Theory
5:256–271.
Paruolo, P. (1996) On the determination of integration indices inI(2) systems.Journal of Econometrics72:313–356.
Paruolo, P. (1997) Asymptotic Inference on the Moving Average Impact Matrix in Cointe-gratedI(1) VAR Systems.Econometric Theory13:79–118.
Reimers, H.E. (1992) Comparison of Tests for Multivariate Co-integration. Statistical Papers33:335–339.
Sephton, P.S., and Larsen, K.H. (1991) Tests of Exchange Market Efficiency: Fragile Evidence From Cointegration Tests.Journal of International Money and Finance
10:561–570.
Tyrvainen, T. (1992) Unions, Wages and Employment: Evidence from Finland.Applied Economics24:1275–1286.
