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Estimation results

Table 2 shows results from the cointegration analysis. On the basis of e.g. various information criteria a lag length of 2 has been chosen. The replacement ratio is assumed to be exogenous from the start with respect to the long-term parameters, and hence the system is partial in that only five out of six variables are perceived as endogenous. The trace test is generally favourable to a rank of 2¹⁾.

The misspecification tests indicate that overall the model is well-specified. The classical distributional assumptions can now be applied to the ongoing statistical analysis, since consists of 2 cointegrating, and thereby stationary, relations. The first test is for exogeneity with respect to the long-term parameters and for whether the variables can be removed individually from the cointegration space²⁾. On the other hand, it does not make sense to apply tests to individual coefficients in and , since as stated they are not identified. A test on the rows in shows that productivity, unemployment and the wedge are exogenous, whereas no variables can be removed from the cointegration space.

The analysis now continues on the basis of a partial system with nominal wages and consumer prices as the endogenous variables, cf. Table 3. Overall the system appears to be well-specified and will be the basis for the ongoing analysis of the cointegrating relationships. The two cointegration vectors, ₁ and ₂, are normalized, but still not identified. The explanatory cointegrating relationships, which conform to the theory, may be the result of linear combinations of ₁ and ₂.

The following focuses on identification of the estimated cointegrating relations, against the background of the theoretical considerations outlined above. Table 4 shows the results of tests of identifying assumptions. A

H0: Rang ( ) =				.. 0			.. 1			.. 2		.. 3			.. 4
Eigenvalues				0,54			0,28			0,25		0,11			0,06
Trace				132,4			67,0			39,6		15,1			5,5
Trace (adjusted for degrees of freedom)1)				116,6			59,0			34,9		13,3			4,8
Critical values, upper2)				87,0			62,9			42,2		25,5			12,2
95 per cent, lower3)				78,5			55,4			35,3		19,4			6,0
Eigenvectors
w				1,00			-0,27			0,37		-1,27			-0,93
pc -ti				-1,64			1,00			-0,35		0,88			1,53
UR				-1,33			0,55			1,00		2,43			-1,13
q				0,23			-1,09			-0,45		1,00			0,57
ww				-2,33			2,65			-0,08		0,00			1,00
r				0,62			0,70			-0,25		-0,25			2,76
Epuation		Loading factors wrt. ..							Std. dev.		Misspecification tests4)
											AR1-55) F(5,60)		ARCH46) F(4,57)	Hetero.7) F(22,42)		Norm.8) (2)
		..	..		..	..		..
w		0,046	0,046		-0,039	0,009		-0,016	0,0065		2,06		1,11	0,47		1,55
pc		0,056	-0,007		-0,033	-0,023		0,031	0,0073		1,72		2,34	1,64		1,16
UR		0,006	-0,009		-0,054	-0,011		-0,009	0,0024		0,39		0,07	0,68		5,75
q		-0,032	0,034		0,791	-0,067		-0,024	0,0154		0,47		0,44	0,91		2,32
ww		0,033	-0,046		0,269	0,090		-0,044	0,0150		1,83		0,66	1,09		16,00**
1) Adjusted for degrees of freedom, see H.-E. Reimers (1992), Comparison of Tests for Multivariate Cointegration, Statistical Papers, vol. 33, pp. 335-359. 2) No drift in the partial system (c=0). c indicates the drift in the partial system relative to the drift in the marginal system standardized by means of the covariance in the respective systems, cf. I. Harboe, S. Johansen, B. Nielsen and A. Rahbek (1995), Test for Cointegration Rank in Partial Systems, Mimeo, Institute of Mathematical Statistics, University of Copenhagen. 3) c=. 4) *, **: Test statistics significant at 5 per cent and 1 per cent levels. 5) LM-test for autocorrelation of order 1-5, F-distributed. 6) LM-test for ARCH of 4th order, F-distributed. 7) F-test based on H. White (1980), A Heteroscedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroscedasticity, Econometrica, 48. 8) Bera-Jarque test for normality, (2)-distributed.

previous study based on quarterly data from Mona finds a relation for wage formation where the rate of wage increases, inter alia, is explained by two non-stationary variables, i.e. unemployment and the replacement ratio³⁾. Therefore these constitute a formal cointegrating relationship. In practice we are probably in a grey area since it is an open question whether the rate of wage increases is stationary or integrated of the first order. It is

H0: Rang () =				.. 0			.. 1
Eigenvalues				0,51			0,22
Trace				81,3			21,2
Trace (adjusted for degrees of freedom)1)				77,4			20,2
Critical values, upper2)				39,6			20,4
95 per cent, lower3)				30,6			11,1
Eigenvectors
w				1,00			-0,73
pc -ti				-1,37			1,00
q				-0,24			0,04
UR				-0,59			-0,73
r				0,64			0,14
ww				-1,55			1,59
Equation		Loading factors wrt. ..							Std. dev.		Misspecification tests4)
											AR1-56) F(5,60)		ARCH46) F(4,57)	Hetero.7) F(22,42)		Norm.8) (2)
			..		..
w			0,058		0,070				0,0066		1,83		1,24	1,00		1,14
pc			0,072		-0,049				0,0061		1,21		0,53	2,08		1,18
Note: See notes to Table 2.

therefore likely that in the longer term the rate of wage increases is negatively correlated and cointegrated with the unemployment rate and positively correlated with the replacement ratio. Columns 1 and 2 show that it still cannot be ruled out that unemployment and the replacement ratio constitute a cointegrating relationship which might also be the only factor affecting the wage equation, with a correct sign.

It is also possible to compile an economically reasonable relationship to describe the real-wage curve, cf. columns 3 and 4. However, this relationship is included in the wage equation with an incorrect sign since the first element of ₁ turns out to be positive in this case, equivalent to no error correction in wage formation. Furthermore, a statistical test shows that in this case the long-term relationship is not the only such term included in

"to be continued"

Footnotes