THE EMPIRICAL VECTOR AUTOREGRESSIVE MODEL 4A. The Data

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

The basic variables in z t suggested by the discussion in Section 3 are: W 5 nominal wages P 5 producer prices N 5 employment Q 5 output volume, which enters as a proxy for the demand shift factor, Z l 2 t a 5 average income tax rate 1 1 s 5 rate of employers’ social security contributions CPIP 5 the price wedge, i.e., the consumer price relative to the producer price, which also proxies the effect of the indirect tax, y P m 5 price of imported raw materials including energy UNION 5 unionization rate, which is a proxy for the bargaining power of the unions. All variables are in natural logarithms and the sample period is 1975:Q1 to 1992:Q2. Some of the data was collected from the WAGE SETTING, TAXES, AND LABOR IN GREECE 179 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 dummies D t that 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, heteroscedasticity, and normality; and 2 the relevance of the conditioning variables in D t . These two aspects of the model are clearly related in the sense that residual misspecification often arises as a consequence of omitting important variables in D t . According to the residual tests reported in Table 1, the bench- mark model for k 5 3 and z t and D t as 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. The estimates of the short-run effects of the conditioning vari- ables are also presented in Table 1. To facilitate readability, coef- ficients with a t-value less than 1.0 have been set to zero. As 180 G. P. Kouretas and L. P. Zarangas Table 1: Residual Misspecification Tests of Model 6 with k 5 3 Eq. s e h 1 21 h 2 2 Skew. Ex.kurt. h 3 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 Dl12t a 0.004 17.3 0.0 0.52 5.91 19.69 Dl11s 0.001 23.5 0.8 1.17 6.57 14.74 DlCPIP 0.009 27.6 2.5 20.49 3.08 3.10 Dlp m 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 Vector D t Eq. D w D p D N D Q D1 2 t a D1 1 s D CPIP D P m DUNION D1 0.011 1 0.001 1 0.005 1 0.018 2 0.023 1 D2 0.043 1 0.015 2 0.003 1 0.022 2 h 1 v is the Ljung-Box test statistic for residual autocorrelation, h 2 v is the ARCH test for heteroscedastic residuals, and h 3 v the Jarque- Bera test for normality. All test statistics are distributed as x 2 with v degrees of freedom. 1 Means significant at the 95 percent level, and 2 at the 99 percent level. WAGE SETTING, TAXES, AND LABOR IN GREECE 181 Table 2: Testing the Rank in the l2 and the l1 Model Testing the joint hypothesis Hs 1 r p-r r Qs 1 rH 9 625.9 497.4 435.6 389.4 355.5 324.6 298.3 276.8 246.9 502.9 454.8 411.2 372.1 332.9 299.5 269.8 243.9 221.9 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 s 2 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 political 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 of L1 trends 5 s 1 and the rank 5 r is tested against the unrestricted H model 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 s9 1 5 p 2 r 2 s 2 , 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 I2 components in the multivariate context. The 95 percent 1 We would like to thank Katarina Juselius for providing us with her preliminary program for conducting the multivariate testing procedure for I2 components. 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 {r 5 0, s 1 5 0, and s 2 5 9} 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 I2 and I1 analysis and the determination of the correct cointegration rank. She argues that the results of the trace and maximum eigenvalue test statistics of the I1 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 for I2 trends, i.e., we estimate the standard I1 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 I2 components. The estimated roots are shown in Figure 1. Table 3 reports the results of the Johansen-Juselius I1 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 2 The 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. 3 A small sample adjustment has been made in all likelihood ratio statistics equal to 22lnQ 5 2T 2 kp o k i 5 r0 1 1 ln1 2 l, as suggested by Reimers 1992. WAGE SETTING, TAXES, AND LABOR IN GREECE 183 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 4 Gonzalo 1994 shows that the performance of the maximum likelihood estimator of the cointegrating vectors is little affected by nonnormal errors. Lee and Tse 1996 have shown similar results when conditional heteroskedasticity is present. 184 G. P. Kouretas and L. P. Zarangas Table 3: Johansen-Juselius cointegration tests 95 Percent critical values r Trace lmax Trace lmax r 5 312.41 1 78.03 1 223.35 66.89 r 1 234.39 1 64.34 1 168.98 60.34 r 2 170.05 1 50.14 1 135.78 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 9.81 1 26.40 1 9.73 1 lp 25.21 1 25.96 1 10.08 1 ln 8.44 1 29.08 1 9.72 1 lq 21.93 1 20.98 1 8.22 1 l 1 2 t a 9.65 1 28.22 1 9.05 1 l 1 1 s 8.20 1 32.90 1 10.02 1 l CPIP 10.34 1 30.55 1 8.93 1 lp m 32.01 1 25.53 1 14.38 1 lunion 17.01 1 26.08 1 14.90 1 Multivariate residual statistics LB17 5 1461.630.06 x 2 18 5 68.980.02 Notes: r denotes the number of eigenvectors. Trace and lmax 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. 1 Indicates statistical significance at the 5 percent critical level. Notes: For the test of exclusion restrictions figures are x 2 statistics with three degrees of freedom, for the stationarity test figures are x 2 with five degrees of freedom, and for the weak exogeneity test figures are x 2 with three degrees of freedom. Notes: LB 5 Ljung-Box statistic for serial correlation with 17 degrees of freedom. x 2 is the Bera-Jarque test for normality distributed with 18 degrees of freedom. WAGE SETTING, TAXES, AND LABOR IN GREECE 185 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 cointegration 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 The model in Section 2 was designed for analysis of wage setting and the demand for labor. As we explained in Section 3, when more than one significant vector has been found, then we must 186 G. P. Kouretas and L. P. Zarangas Figure 3. Test of known beta eq. to betat. 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: logW 5 b P logP 1 b N logN 1 b Q logQ 1 b t a log1 2 t a 1 b s log1 1 s 1 b y logCPIP 1 b P m logP m 1 b U logUNION 11 For this relation to be considered as a wage-setting schedule the signs should be: b P 0, b Q 0, b t a 0, b s 0, b y 0, b U 0, and possibly b P m 0. There are two extreme hypotheses that could be considered regarding wage setting. The first one takes the unions as having WAGE SETTING, TAXES, AND LABOR IN GREECE 187 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: 2b t a 5 b y 5 1 1 b s 5 v 12 in Equation 11, which is a standard way to proceed when no distinction is made between proportional and marginal income tax rates. If v 5 1, the taxes fall fully on the firm. If v 5 0, they fall fully on the worker. In Table 4 we give the full set of restrictions imposed on the wage equation. Equation 11 can also be used to describe the demand for labor relation because this equation is in fact a vector of nine endogenous variables. Thus, if we now normalize this vector with respect to logN, then we receive a demand for labor equation. In this case, 188 G. P. Kouretas and L. P. Zarangas Table 4: FIML Estimated Coefficients and Identification Wage setting Labor demand Output Coeff. Variables b i a i b i a i b i a i b w W 1.000 0.003 20.163 20.100 1.260 20.008 b P P 21.616 0.022 0.523 20.014 21.912 20.002 b N N 1.045 0.015 1.000 20.012 20.414 0.018 b Q Q 21.955 0.041 21.142 0.125 1.000 0.009 b ta 1 2 t a 2.283 20.007 20.032 20.004 22.854 0.005 b s 1 1 s 2.840 20.001 25.401 0.009 1.640 0.001 b y CPIP 22.704 20.011 20.338 0.045 2.300 20.009 bP m P m 2.007 20.036 20.506 0.033 1.153 20.001 b U 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 b w 5 2b P 5 b w 5 2b P b w 5 2b P b w 5 2b P 5 b w 5 2b P 5 2b Pm 5 b ta , 2b Pm 5 b N 5 2b Pm 5 b s , b s , b ta 5 2b y , b N 5 2b Q , 2b Q 5 2b ta , b ta 5 b ye 5 b ta 5 b y 5 b N 5 2b Q , b ta 5 1 2b s 5 b ta 5 1 2b s 5 b U 5 0 b Pm 5 b U 5 0 b s 5 b Pm 5 2b y 2b y b U 5 0 x 2 5 1.03 x 2 5 5.03 x 2 5 7.33 x 2 5 3.99 x 2 5 5.78 Q 16 5 11.59 Q 16 5 10.45 Continued WAGE SETTING, TAXES, AND LABOR IN GREECE 189 Table 4: Continued Estimates of the impact of cumulated innovations in variable j, on variable k kj w P N Q 1 2 t a 1 1 s CPIP P m 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 1 2 t a 0.012 20.100 0.073 0.079 20.171 20.352 0.002 0.1 0.002 1 1 s 0.011 0.006 0.014 20.005 0.017 0.113 0.038 20.0 0.000 CPIP 0.035 20.111 0.381 0.162 20.254 21.335 0.331 0.2 0.006 P m 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 are x 2 distributed with 5, 6, 6, and 8 degrees of freedom respectively. Q. is the Johansen and Juselius 1994 test for overidentifying restrictions and is a x 2 distributed with 16 degrees of freedom. Notes: The t-values for the impact-matrix for the MA representation can be found in Paruolo 1997. 190 G. P. Kouretas and L. P. Zarangas the expected signs of the coefficients should be b w 0, b P 0, b Q 0, b ta 5 0, b s 0, b y 5 0, and possibly b Pm 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, then b y ? 0. The restriction b w 5 2b P 5 2b Q 5 b s . 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 write b w 5 2 b P 2 b Pm 2 b Q 5 b s . 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