WAGE SETTING, TAXES, AND LABOR IN GREECE 173
2. THE ECONOMIC MODEL
There are n identical firms, which have a production function Q 5 F
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 5 P ˆ [Z˜FN,m,K]FN,m,K 2 W1 1 sN 2 P
m
m 1
where Q ˆ
d
5 pˆ
2
1
PZ ˜
2
1
; DPZ is a downward sloping demand curve of the separable form introduced by Nickell 1978. Here,
Z 5 Z ˜
2
1
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, P 5 competitors’ producer price, W 5
nominal consumer wage, s 5 payroll tax, P
m
5 price 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:
N
d
5 N
d
1
W 1 1 s
P ,Z,
P
m
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, U 5 UW1 2 tP
c
,N,B, where P
c
is the consumer prices, t is the income taxes, and B is the replacement ratio unemployment benefit in real terms. The
partial derivatives of this general preference function are:
U9
1
,U9
2
,U9
3
. 0 and U ″
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
U 2 U
u
p 2 p
1
2u
s.t.N . 5 arg
N
maxp 3
174 G. P. Kouretas and L. P. Zarangas
where u refers to the bargaining power of unions, 0 , u , 1. U 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 the U
depends on strike allow- ances, U
5 U A. p
is the fall-back profit that reflects fixed costs during a production stoppage. When p
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 5 WP,s,t,
P
c
P ,u,P
m
,Z,B,A,K,t 4
Indirect tax, y exerts an influence as part of the price wedge, P
c
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 the Z
it
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 variables D
t
5 [d
1t
, . . . , d
qt
] 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:
Dz
t
5 G
1
Dz
t
2
1
1 . . . 1 G
k
2
1
Dz
t
2
k
1
1
1 Pz
t
2
k
1 gD
t
1 m 1 e
t
5
where e
t
| Niid
p
0,S. The parameters G
1
, . . . , G
k
2
1
,g define the short-run adjustment to the changes of the process, whereas P 5
ab9 defines the short-run adjustment, a, to the cointegrating rela- tionships, b. If the short-run effects are basically different from the
long-run effects, due, for instance, to costly arbitrage or imperfect information, the explicit specification of the short-run effects is
WAGE SETTING, TAXES, AND LABOR IN GREECE 175
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, . . . , G
k
2
1
,P,g,m,S varies unrestrictedly, it follows that the I1 and the I2 models are submodels of 5. In the
unrestricted form, therefore, model 5 corresponds to the I0 model. Hence, in the statistical sense the I0 model is the most
general, because the higher order models are nested in this model. For simplicity we assume k 5 2 in all subsequent discussions of
model 5, i.e. Eq. 6,
Dz
t
5 G
1
Dz
t
2
1
1 ab9z
t
2
2
1 gD
t
1 m 1 e
t
6
3A. The I1 Model
Johansen 1991 shows that if Z
i
| I
1, the following restrictions on model 6 have to be satisfied Eq. 7:
P 5 ab9, 7
where P has reduced rank, r, a, and b are p 3 r matrices, and Eq. 8
C 5 a
⊥
2I 1 G
1
b
⊥
5 wh9, 8
where C is a p-r 3 p-r matrix of full rank, w and h are p-r 3 p-r matrices, and a
⊥
and b
⊥
are p 3 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 representation 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. The I2 Model
If condition 8 for the I1 model is violated, the process Z
t
is integrated of second order or higher. When the process is I2, it
is useful to rewrite model 6 in second differences Eq. 9:
D
2
z
t
2
1
5 GD
t
2
1
1 ab9z
t
2
2
1 gD
t
1 m 1 e
t
9
176 G. P. Kouretas and L. P. Zarangas
where G 5 2 I 1 G
1
and ab9 has reduced rank r. If Z
t
| I
2, the following restriction on the parameters of model 9 has to be
satisfied Eq. 10:
C 5 a9
⊥
Gb
⊥
5 wh, 10
where w and h are p-r 3 s
1
matrices and s
1
, p 2 r. Johansen 1997 shows that the space spanned by the vector Z
t
can be decomposed into r stationary directions, b, and p 2 r nonstationary directions, b
⊥
, and the latter into the directions b
1 ⊥
,b
2 ⊥
, where b
1 ⊥
5 b
⊥
h is of dimension p 3 s
1
and b
2 ⊥
5 b
⊥
b9
⊥
b
⊥
2
1
h
⊥
is of dimesnion p 3 s
2
and s
1
1 s
2
5 p-r. The properties of the process are described by
I 2:
h
b
2 ⊥
j
, I
1:
h
b9z
t
j
,
h
b
1
9
⊥
j
, I
0:
h
b
1
9
⊥
Dz
t
j
,
h
b
2
9
⊥
D
2
z
t
j
,
h
b9
z
t
1 v9Dz
t
j where v is a p 3 r matrix of weights, designed to pick out the
I 2 components of Z
t
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 the I2 model. Furthermore, Johansen
1995a provides an asymptotically equivalent two-step procedure that is computationally simpler. It applies the standard eigenvalue
procedure derived for the I1 model twice: first to estimate the reduced rank of the P matrix, and then, for given estimates of a
and b, to estimate the reduced rank of aˆ9
⊥
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.
The necessary and sufficient conditions for identification in a cointegrated system in terms of linear restrictions on the columns
of the accepted eigenvectors, b, are analogous to the classical identification problem. Thus, the order condition for identification
WAGE SETTING, TAXES, AND LABOR IN GREECE 177
of each of the r cointegrating vectors is that we can impose at least r 2 1, 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 the ith cointegration vector, the Rank condition, is that the rank b9H
i
5 r 2 1, where H
i
is 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 as x
2
with v 5 S
i
pl 2 r 1 1 2 s
i
degrees of freedom, where pl is the number of freely estimated parameters in b
i
.
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 parameters G
i
, i 5
1 . . . k, are fixed to their full sample values and only the long- run parameters in Equation 6 are reestimated.
The first test is called the Rank test, and we examine the null hypothesis of sample independency of the cointegration rank of
the system. This is accomplished by first estimating the model over the full sample, and the residuals corresponding to each
recursive subsample are used to form the standard sample mo- ments associated with Johansen’s reduced rank. The eigenvalue
problem is then solved directly from these subsample moment matrices. The obtained sequence of trace statistics is scaled by
the corresponding critical values, and we are unable to reject the null hypothesis that the chosen rank is maintained regardless of
the subperiod for which it has been estimated if it takes values greater than one.
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 a x
2
distributed with p-rr degrees 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
Kategori