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Tests of hypotheses on and , 1975-1995

Eigen- vectors	1.		2..		3.		4.		5.		6.		7.
w	0	1	0	1	1	1	1	1	1	0	1	0	1	0
pc -ti	0	-1,37	0	-1,37	-1	-1,43	-1	-1,37	-1	0	-1	0	-1	0
q	0	-0,16	0	-0,18	-1	-0,06	-1	-0,18	-1	0	-1	0	-1	0
UR	1	1,19	1	-0,05	-9,41	1,26	-13,20	-0,06	5,44	1	-10,90	1	0,78	1
r	-0,70	-0,50	-0,56	0,36	5,47	-0,36	7,21	0,36	-2,59	-0,75	5,97	13,54	0,84	-0,56
ww	0	-1,82	0	-1,76	1,71	-2,25	2,73	-1,76	-1,12	0	2,10	0	-1,01	0
Loading factors:
w	-0,11	-0,02	-0,15	0	0,01	-0,00	0,01	0	-0,02	-0,03	0,01	0	0	-0,15
pc	-0,14	0,10	0	0,11	0,01	0,09	0	0,11	0,07	-0,35	0	0,01	0,08	0
LR-test*)	(3)=1,13		(4)=2,40		(1)=0,11		(2)=0,13		(5)=9,72		(6)=25,87		(6)=11,36
	[0,77]		[0,66]		[0,74]		[0,94]		[0,08]		[0,00]		[0,08]
Note: Statistics in square brackets indicate marginal significance levels.

the wage equation. It should be noted that certain coefficients in the realwage equation, e.g. to the replacement ratio, have values impossible to interpret if they are estimated freely. This must of course be seen against the background of the fact that the coefficients for the unemployment rate and the replacement ratio are not identified in the real-wage equation in column 5, so interpreting these coefficients is not relevant. On this basis the real-wage curve cannot be rejected.

In the remaining columns the two types of relationship are identified simultaneously in the cointegration space. A Phillips curve equivalent to ₂ in column 7 also appears to dominate here, cf. a comparison of LR-tests of the overall set of overidentifying restrictions in columns 6 and 7.

The initial cointegration analysis appears to favour the Phillips curve specification rather than a real-wage equation. Nevertheless, the dynamic analysis continues to apply both hypotheses, cf. Table 5. This analysis is based on single-equation estimations¹⁾ and on the general-to-specific principle.

In principle, a real-wage equation with reasonable statistical properties can be estimated. However, conventional encompassing tests show clearly

Dynamic wage equations, 1975-1995. Endogenous variable: w.

Exogenous	1.		2.		3.		4.		5.		6.
Constant	0,05	(5,76)	0,06	(6,47)	0,06	(6,25)	0,05	(5,83)	0,05	(7,65)	0,05	(7,54)
pC,-2	0,14	(1,57)					0,10	(1,23)
pC,-3	0,19	(2,11)	0,20	(2,21)	0,20	(2,18)	0,16	(1,81)	0,18	(2,07)	0,18	(2,06)
(py -pc ) -3	0,12	(2,83)	0,14	(3,11)	0,14	(3,08)	0,13	(2,96)	0,14	(3,16)	0,14	(3,15)
h	-0,77	(-4,29)	-0,84	(-4,85)	-0,84	(-4,80)	-0,78	(-4,39)	-0,84	(-4,86)	-0,85	(-4,83)
UR					-0,02	(-0,10)					-0,06	(-0,27)
UR-1	-0,14	(-2,62)	-0,14	(-2,49)	-0,14	(-2,47)	-0,13	(-2,36)	-0,13	(-2,37)	-0,13	(-2,37)
r-1	0,05	(3,10)	0,06	(3,88)	0,06	(3,75)	0,05	(2,97)	0,06	(3,82)	0,06	(3,70)
ec-11)	-0,02	(-1,25)	-0,01	(-0,78)	-0,01	(-0,74)
Test statistics:
R2	0,72		0,71		0,71		0,71		0,70		0,70
	0,0060		0,0061		0,0061		0,0061		0,0061		0,0061
DW	2,33		2,34		2,34		2,33		2,34		2,34
Auto- correlation2)	0,82		1,02		1,00		0,85		1,02		1,01
ARCH3)	1,11		1,29		1,30		1,33		1,29		1,35
Heterosce.4)	1,03		0,76		0,63		0,94		0,61		0,51
Norm.5)	4,42		3,75		3,81		2,27		2,66		2.84
1) . The results in this table are based on corresponding to a longterm relationship between product real wages, unemployment and level of compensation. However, other values  of give generally equivalent results. 2) LM-test for autocorrelation of order 1-5, F-distributed. 3) LM-test for ARCH of 4th order, F-distributed. 4) F-test based on White (1980), op.cit. 5) Bera-Jarque normality test, (2)-distributed.

that the Phillips curve dominates the real-wage equation, since the equivalent coefficient to the wage share is not significant (columns 1 and 2). Furthermore, a test for hysteresis²⁾ (columns 3 and 6) was made by studying in the traditional way whether changes in unemployment rather than levels determine the wages. This does not seem to be indicated. On the basis of the above analysis a Phillips curve (columns 4 and 5) is preferred.

The preferred equation (column 4) has satisfactory statistical properties. There are no signs of autocorrelation and it cannot be ruled out that the error term is normally-distributed white noise. It should be noted that a standard deviation in the quarterly logarithmic changes of 0.0061, or approximately 0.6 per cent, converted into percentage year-on-year changes is equivalent to just over 1.2 per cent. This is of course a relatively large degree of uncertainty, but it should be viewed in the light of the relatively volatile quarterly rate of wage increases. In general, the model-determined wage development seems overall to give a satisfactory description of the actual development within the estimation period, cf. Chart 3, although it does not capture all fluctuations.

Stability and forecast properties

Outside the estimation period, i.e. from expiry of the estimation period at end-1995 to the 4th quarter of 1997, which is the latest statistics-based period, the estimated Phillips curve also performs relatively well, cf. Chart 3. The forecasts are not especially accurate all the way through, but the curve does come close to the "peaks" of the quarterly wage increases in 1993 and 1995, and not least the dampened wage development in the second half of 1996. It should furthermore be noted that even when the estimation period runs only to 1992 the Phillips curve gives a relatively good description of the wage increases throughout the 1990s.

On the basis of the recursive estimates in Chart 5 the stability properties of the estimated Phillips curve appear to be satisfactory. The various Chow tests do not indicate any significant problems of structural breaks in the estimation period³⁾. The coincidence of low wage increases in recent years and a continuing decline in unemployment does not appear to give the model problems, although a small absolute drop in the coefficient for the unemployment rate after 1993 is observed. At present the unemployment rate is at the same level as the low in the mid-1980s, while the current price increases contribute to lower wage increases than previously. However, the fact that the model-determined rate of wage increases is not higher is due primarily to the absence of any contribution from reductions of working hours, as was the case in 1987-1991, cf. Chart 2.

Regarding the obvious stability of the Phillips curve in the period from 1975 until today it should be stated that the wage reaction to changes in the unemployment rate is more than trebled when the years 1972-1974 are included in the estimation period. This has no significant impact on the other

coefficients and the stability properties of the equation likewise seem good. This indicates that during the first oil crisis the Danish labour market, like many other western European countries, experienced a change in regime from an unemployment rate of around 2 per cent to a situation where the unemployment rate more than trebled, simultaneously with a strong upswing in the rate of wage increases. This may have led to a structural break in the Phillips curve, and hence favours the use of a sample which starts in 1975.

Footnotes