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An Employment Equation for Belgium
V. Bodart, Ph. Ledent and F. Shadman-Mehta
Discussion Paper 2009-16
An Employment Equation for Belgium
Vincent Bodart
Philippe Ledent
Fatemeh Shadman-Mehta ∗
ECON-IRES
Universit´e catholique de Louvain
June 10, 2009
Abstract
Economic theory considers economic growth and wage costs as crucial
determinants in the process of job creation. In this paper, we try to quantify
the relationship that exists between these variables in Belgium. Our objec-
tive being mainly the use of the empirical model for forecasting purposes,
we use a V AR model to enable us to apply statistical tools to test some
possible constraints within a loose model. We analyse the relationship at
three levels: one national and two sectoral.
Keywords: Employment growth, long-run equilibrium, V AR model.
JEL classification: C32, C52, E24, E27.
∗We are grateful to Muriel Dejemeppe and Bruno Van der Linden for their comments on a
first version of this paper, presented at the S´eminaire de Politique ´
Economique at the Economics
Department. We are further indebted to Bruno Vanderlinden for his precious comments that
have helped improve greatly this version. Any remaining errors or shortcomings are ours.
1 Introduction
This paper is aimed at evaluating the relationship between employment and eco-
nomic growth and wages in Belgium. The assertion that economic growth should
affect employment positively is well documented in the economic literature. Our
objective here is to concentrate on determining empirically the nature of this re-
lationship. We will therefore consider questions such as the short and long-run
impacts of growth on employment as well as how the adjustment process is spread
over time. Changes in employment as a result of changes in production are indeed
considered to take time. This may either be due to adjustment costs resulting from
the hiring and firing of employees, or to uncertainty with regards to the permanent
nature of new production levels.
Economic growth is clearly not the only variable that affects employment. Wage
costs are equally important and are expected to have a negative impact: the higher
the cost of labour, the more firms will substitute labour by less costly production
factors. A firm can also increase its production by improving the productivity of
its labour force, for example by modernising the production process.1
Our efforts here will be focussed on estimating a simple three-variable model ex-
plaining the behaviour of employment, output and wages in Belgium. We will
estimate the model over the period 1980:I to 2002:IV. We will then use the model
to produce forecasts of employment levels under certain scenarios regarding eco-
nomic growth and wage settlements over the period 2003:I to 2007:I and compare
those results to the actual employment levels achieved during that period, the aim
being to evaluate the possible contribution of some measures such as the reduction
of labour costs through lower social security contributions.
The main contribution of the paper is to investigate how economic activity and
labour costs affect employment in Belgium. As far as we know, there is indeed no
study providing such evidence for Belgium. A particular feature of our study is to
examine this relationship both at an economy-wide and at a sectoral level, while
in most emiprical studies, the evidence is only provided for the overall economy.2
The paper is organised as follows. Section 2 explains the data and related difficul-
ties. Section 3 summarises the methodology used. Section 4 reports the estimated
results. The estimation is done at three levels, one national and two sectoral levels.
Section 5 investigates the implications of the estimated models in out-of sample
forecasts. Section 6 concludes.
1Formally, the dependence of employment on output, real labour costs and labour productivity
can be derived from the maximisation of a production function with two production factors,
labour and capital. See for instance Dixon et al. (2004), p.17-20 and Moure (2004), p.8-10.
2See for instance Moure (2004) for the euro area, Dixon et al. (2004) for Australia, Prachowny
(1993) for the United States and Decressin et al. (2001) et. al. for France, Germany, Italy.
1
2 Data
Over the last few years and driven by the unified national accounting rules imposed
by Eurostat, the Belgian national accounts data, including employment levels and
wage bills, have undergone major revisions. As a result, it is no longer possible to
have data series which are both recent and long enough on our three variables of
interest, namely the GDP, employment and wages. Given the necessity of using a
large enough sample in order to be able to depict meaningful long-term relations
between these variables, we have opted for using the older quarterly data on the
three variables which still constitute a homogeneous set over the period 1980 to
2002.3The revised data go back only to 1995.
Apart from the period over which suitable data are available, there is one more
problem which will affect our results. In the literature on this subject, the normal
approach is to use the volume of hours worked for employment and hourly wage
rates for wage costs.4The reason is simply that firms first determine the volume
of hours of work they need, based on the hourly wage rates they have to pay. It
is only then that they translate this into the number of persons to employ, as this
can vary within the legal limits imposed.
In our case, we could not obtain suitable data on hours worked and hourly wage
costs which would cover the whole period or have a quarterly frequency. As a result,
the employment variable we use is total employment (employees and independents,
including those nationals working at the border regions) expressed as the number of
persons in employment. As for the wage cost variable, we obtain the wage cost per
employed person by dividing the quarterly series for the wage bill by the number
of persons in salaried employment.5Clearly, this implies that both these variables
are affected by the evolution of the average number of hours worked per employed
person during this period. Aware that this is a major shortcoming, we have tried
to face this problem by including in our models a variable which is an estimate of
the average hours worked. We found however that this variable had no significant
effect and our results reported here therefore do not include it. We are nevertheless
conscious that the analysis of the evolution of wage costs as suggested by our
model may be reflecting various possible sources of change, namely centralised wage
negotiations, various government measures taken to alleviate employers’ social
security contributions but also changes in the average number of hours worked per
3These older series have been revised not because of poor quality, but in order to conform to
new national accounting rules.
4See Dixon et al. (2004) amongst others.
5Similar definitions are used for sectoral employment and real wages.
2
employed person.67
We note finally that both the wage cost and GDP variables are in real terms. The
deflator used is either the GDP deflator in the case of the national results, or the
deflator of the sectoral value added in the case of sectoral data.
The analysis presented in this paper is done on the rates of growth of the different
series. We did at first try to estimate the model so as to find a long-term rela-
tionship between the levels of the three variables. We could not however find any
evidence of cointegration between them and decided therefore to proceed with the
growth rates.8Table 2.1 shows some descriptive statistics on the three variables
used in our study. As mentioned earlier, our analysis is done at the national level
and for the two most important sectors in Belgium, namely industry and services.9
Mean Median Standard
Deviation
Quarterly growth rate of output
National 0.52 0.61 0.70
Industry 0.47 0.47 1.21
Services 0.59 0.60 0.70
Quarterly growth rate of employment
National 0.15 0.12 0.35
Industry -0.39 -0.42 0.47
Services 0.43 0.41 0.48
Quarterly growth rate of wage costs
National 0.33 0.27 0.96
Industry 0.86 0.94 1.28
Services 0.14 0.18 1.39
6Detailed information on wage formation in Belgium can be found in Burggraeve and Caju
(2003), p. 8-10. We shall simply remind the reader here that in Belgium, wages are settled
through negotiations that are held successively at three levels: national, sectoral and firm level.
These negotiations have to comply with three important institutional characteristics: an overall
guaranteed minimum wage, the automatic indexation of gross wages and a maximum imposed on
the growth rate of nominal hourly labour costs. In the past, labour tax reductions have played
an important role in slowing down the growth of labour costs in Belgium. The tax wedge in
belgium remains however important. According to the OECD estimates ( OCDE (2008)), it is
the highest in Europe (EU15).
7Everything equal, the growth rate of the wage costs per person employed will be lower when
the number of people working part-time increases.
8We would have expected to find cointegration in the levels of the variables. The inability to
reject the null hypothesis of no cointegration in the levels is most probably due on the one hand
to a small sample, and on the other, to the problem of the appropriate definition of the variables
of interest as mentioned at the start of this section. We plan to revisit this problem as and when
more data become available.
9This refers to services in the private sector, including commerce, finance, insurance, transport
and communication. In 2002, which is the last year of our estimation period, the share in GDP
of private services and manufacturing industries were respectively 53% and 18.5%, compared to
42.6% and 26.3% in 1980. In 2002, 54.3% of the total number of persons in salaried employment
was employed in private services and 18.5% was employed in manufacturing industries.
3
Table 2.1: Descriptive Statistics, sample: 1980:I-2002:IV.
The table shows that over the period considered, Belgian GDP grew at an average
quarterly rate of 0.5%, equivalent to an annual rate of roughly 2%. During this
period, employment grew at a much slower pace of 0.15% per quarter (0.6% per
annum), while wage costs grew at double that rate, i.e. 0.33% per quarter. When
we consider the sectoral results, we note that the growth rate of value added in
both sectors is not so different from GDP. On the other hand, the movement of
employment and wage costs has been very different in these sectors. Over the
period 1980:I-2002:IV, employment in Industry fell by an average of 0.4% per
quarter (1.5% per annum), while the opposite happened in the Services sector,
where employment increased by the same rate.10 On the other hand, wage costs
have increased much more sharply in Industry (0.9% per quarter) than they did
in Services (0.1% per quarter). This observed fact may be due to differences in
the evolution of hourly wages or productivity growth. It may also be reflecting
structural differences such as standard hours, reduction of social security contri-
butions, the development of interim and part-time employment, ··· A look at the
standard deviations in Table 2.1 also shows that employment is less volatile than
economic activity, that is fluctuations in activity do not create equally important
fluctuations in employment. Wage costs on the other hand appear to be much
more volatile.
3 The methodological framework
The approach we have taken here is to study a V AR system composed of the
three variables of concern, i.e. employment l, output yand wages w.11 AV AR
model essentially treats all variables in the system as endogeneous. Given that
all explanatory variables are lagged values of the endogeneous variables in the
system, simple estimation by OLS provides consistent and asymptotically normally
distributed estimators, so that statistical inference may be applied in the usual way.
The most important factor in the choice of the variables that enter a V AR is
economic theory. Our choice of l,yand was the basis of our V AR model reflects
our main interest here to estimate labour demand as a factor of production. A
second factor, which is not negligible in practice, is the limited size of available
data. Finally, if too many variables are included in the system, the number of
coefficients becomes very large and much inefficiency may be introduced in the
estimated coefficients. If the main purpose of using a V AR model is to produce
forecasts, this can be a serious problem. Given our interest in developing this
simple model to evaluate its usefulness for forecasting future trends in employment
10The reduction in industrial employment in Belgium is generally explained by the move to
the tertiary sector, but also by the shift outside the sector of various previously internal service
activities, such as cleaning, personnel management, etc ···
11Lower case letters denote logarithms of actual variables. For example, l=Ln(L).
4
in Belgium, there was further reason to keep the number of endogeneous variables
in the system to a minimum.
As we found no satisfactory evidence of any long-term relationship, we concentrate
our analysis on the growth rates of the three series. We report here the results
for the quarterly growth rates. We have done a similar analysis for the annual
growth rates, but the overall conclusions do not change substantially.12We have
also done the analysis at three different levels. The first one is at the national level.
The other two deal with the two most important sectors in the Belgian economy,
namely Industry and Services.
4 Empirical Results
The sample used for the results shown below covers the period 1980:I to 2002:IV.
Data on employment and the GDP are available for periods beyond 2002:IV. How-
ever, due to changes in the definition of these variables, the available data are not
always consistent with the earlier period. Moreover, the same is not true about
the wage bill, which is not yet available at all beyond 2002:IV. We can therefore
not calculate wage costs per head beyond 2002:IV.
4.1 Total Employment
We begin by estimating the unconstrained reduced form of the model. The vari-
ables included in the model are ∆l, ∆yet ∆w. Our first task is to check that we
are dealing with a system of stationary variables. To this end, we test for coin-
tegration using Johansen’s tests on the estimated V AR model.13 The results are
reported in Table 4.1.1. They show that this V AR system is indeed stationary.
rank Trace test[Prob] Max test[Prob] Trace test(T-nm) Max test(T-nm)
0 48.85[0.000]∗∗ 22.16[0.034]∗36.34[0.007]∗∗ 16.48[0.206]
1 26.69[0.001]∗∗ 20.13[0.004]∗∗ 19.86[0.009]∗∗ 14.97[0.037]∗
2 6.57[0.010]∗6.57[0.010]∗4.89[0.027]∗4.89[0.027]∗
* means significance at 5% and ** at 1%
Table 4.1.1: Johansen tests for cointegration, at the national level.
Our next task is to estimate the model by maximum likelihood so as to be able to
test a certain number of restrictions to simplify the model and reduce the number
of parameters. Given that our main focus in this paper is on employment, we only
report here the estimated employment equation. Table 4.1.2 shows the result of
the most parsimonious equation obtained. Throughout the reduction process, we
12Interested readers can obtain these results from the authors.
13See Johansen and Jeselius (1990). The empirical results reported in this paper have been
obtained using the software Oxmetrics.
5
have kept a close eye on misspecification tests which are reported at the bottom of
the table. In this table as in the tables that will follow, Normality is the statistic
proposed by Doornik and Hansen (1994) to test if the residuals of an equation
could be from a normal distribution. P ortmanteau refers to the Box and Pierce
(1970) statistic for testing for autocorrealtion. This statistic is only valid in a
single equation context, but is reported anyway. AR :Fis the more appropri-
ate LM test for autocorrelated residuals. ARCH :Fis the LM test proposed
by Engle (1982) for Autoregressive Conditional Heteroscedacity or autocorrelated
squared residuals. Hetero :Fis the statistic proposed by White (1980) to test
the hypothesis of unconditional homoscedasticity against the alternative that the
variance of the errors depends on the regressors and/or their squares.
Coefficient Std error p-value
Constant -0.063 0.039 0.12
∆l−10.606∗∗ 0.090 0.00
∆l−2−0.415∗∗ 0.125 0.002
∆l−30.387∗∗ 0.096 0.000
∆l−4−∆l−5−0.25∗0.10 0.017
∆l−6−∆l−7-0.16 0.09 0.084
∆y−10.134∗∗ 0.031 0.000
∆y−20.078∗0.032 0.017
∆y−3+∆y−50.076∗∗ 0.023 0.002
∆w−2−0.051∗0.023 0.032
∆w−3-0.042 0.023 0.077
∆w−6+∆w−7−0.044∗0.019 0.026
T=82(1982:(3)-2002(4)), σ= 0.18%, Portmanteau(6)=2.08, N ormality :χ2(2) = 2.7
AR :F(6,54) = 1.27, ARCH :F(10,54) = 2.44∗,Hetero :F(42,31) = 0.83
ARvec :F(54,161) = 0.67, Normalityvec :χ2(6) = 8.35, H eterovec :F(252,163) = 0.64
LR :χ2(40) = 13.704
* means significance at 5% and ** at 1%
Table 4.1.2: The quarterly growth of employment in Belgium.
The equivalents of these statistics for the system as a whole are reported with a
vec superscript. Finally, LR :χ2is the likelihood ratio test of the over-identifying
restrictions imposed on the system as a whole. A look at the statistics reported
for the employment equation shows that practically all mis-specification tests are
satisfactory. There is only some heteroscedasticity in the errors of the employment
equation which might signal the need for a longer maximal lag. Further evidence of
the reasonable fit of the equation estimated in the sample is provided in Figure 4.1.
The upper part of Figure 4.1 shows the actual and fitted values and the lower part
shows the residuals scaled by their estimated standard error. The latter remain
mainly (except for two observations) within ±2ˆσ. We also estimated the system
recursively to check for possible structural shifts in the relationships as a result of
various policies implemented by the Belgian government in this period. No such
breaks are detected.
6
It is worth noting from Table 4.1.2 that an increase in the rate of growth of the
economy has a positive effect on employment growth in the long-run. And an
increase in the growth rate of wages has the opposite effect. In each case, the
impact on employment is persistent.
1985 1990 1995 2000
−1.5
−0.5
0.5
1.5 Dl Fitted
1985 1990 1995 2000
−2
0
2
scaled residuals Dl
Figure 4.1: The quarterly growth of employment in Belgium.
One way of analysing the effects of past shocks on current variables in a dynamic
system of variables is through a look at the impulse response functions. This
amounts to looking at the dynamic multipliers implied by the system, when the
shock in question can be treated as exogenous. If these multipliers turn out to
be different from zero, then a response is depicted from one variable to another.
When a dynamic system is stable, such dynamic mulitpliers usually die out quite
quickly.
There are various ways of approaching the impulse response analysis. The simplest
is to look at the system after an innovation of one unit in only one of the variables
in the system and trace out the dynamic multipliers. However, if the variables
in the system happen to be measured in different scales, and when we want to
analyse the responses of each and every variable to possible shocks in the other
variables in the system, applying the same innovation of one unit each time is not
very helpful for comparing the effects. To correct for this problem, a rescaling
of the multipliers is required, which can be achieved by considering innovations
of one standard deviation. Finally, if the shocks in different variables are not
independent, then a shock in one variable in the system will be accompanied by
a shock in other variables and the dynamic multipliers calculated above will be
7
misleading. An orthogonal transformation of the V AR model is then required to
create a system with independent errors. This final approach however comes with
its own problems. The transformation, based on the Choleski decomposition of
the initial variance-covariance matrix, is not unique and depends on the order in
which the variables appear in the system.14
In the impulse response analysis presented here, we have opted for shocks of one
standard deviation. The results are presented in the Appendix and are summarised
in graphs which show the accumulated responses after an innovation of one stan-
dard deviation for each variable. A look at the Figures in the Appendix makes
it clear that there is great variation in the standard errors of the equation errors.
Whereas at the national level, the largest standard error is that of the innovations
in the growth rate of wages which still remains well below one, the situation is
very different at the sectoral level. It is particularly striking in the Service sector,
where the standard error of the innovation in sectoral wages is four times larger
than that in sectoral employment.15
Figure A.1.b shows clearly that a one time increase in the growth rate of the
GDP leads to the accumulated effect over time of an increase in the growth of
employment of about the same order of magnitude. It takes about twenty quarters,
i.e. five years, for this adjustment to be completed. Such a shock also leads to a
positive but modest increase in the growth of wages, even though the initial effect
is negative. It takes about ten quarters, i.e. two and a half years, before this effect
becomes apparent. Similarly, we can see in Figure A.1.c that a one time increase
in the growth rate of wages leads over time to the accumulated effect of a decline
in the growth of employment which is of the same order of magnitude and which
also takes about twenty quarters to take its full course. Notice also that such a
shock has a negative impact on the growth of the GDP which is more substantial
than the effect of increased GDP on wages.16
4.2 Employment in Industry
In this section, we repeat the exercise, but this time applied to the Belgian in-
dustrial sector. The main objective is to see if this sector’s employment behaves
more or less as at the national level, or whether discernible differences exist. The
relation to the sectoral real wage is of particular interest.
14An impulse response analysis can not really be a very reliable source for a structural inter-
pretation of a model. It plays a more useful role in a forecasting exercise where the dynamic
multipliers are of interest. See L¨utkepohl (1993) and Hendry (1995).
15We did also look at the orthogonalised system, but found that no major changes occur in the
impulse responses. The ordering reported in this paper consists of the system ∆l, ∆y, ∆w. The
estimated equation errors display little correlation between them. For the sake of robustness, we
have also verified other orderings and found that the covariance matrix of the V AR innovations
continues to remain approximately diagonal.
16The figures in the appendix are the accumulated and not the simple impulse responses. It
is the latter which would tend to 0 in a stable system.
8
We begin by estimating the unrestricted reduced form. The variables in the model
are now ∆lInd , ∆yInd et ∆wInd .17Johansen’s tests for cointegration confirm the
stationarity of the system. The results are given in Table 4.2.1:
rank Trace test[Prob] Max test[Prob] Trace test(T-nm) Max test(T-nm)
0 54.21[0.000]∗∗ 30.74[0.001]∗∗ 40.33[0.002]∗∗ 22.87[0.026]∗
1 23.47[0.002]∗∗ 16.93[0.017]∗17.46[0.023]∗12.59[0.090]
2 6.54[0.011]∗6.54[0.011]∗4.87[0.027]∗4.87[0.027]∗
* means significance at 5% and ** at 1%
Table 4.2.1: Johansen’s tests for cointegration, in Industry.
Maximum likelihood estimation of this system allows us to test some restrictions
and reduce the number of parameters to estimate. The reported model in Table
4.2.2 passes satisfactorily all misspecification tests as seen from the statistics
Coefficient Std error p-value
Constant -0.0625 0.083 0.46
∆lInd
−10.635∗∗ 0.10 0.00
∆lInd
−2−0.353∗∗ 0.114 0.003
∆lInd
−3+ ∆lInd
−50.292∗∗ 0.075 0.000
∆lInd
−4-0.21 0.114 0.067
∆yInd
−10.12∗∗ 0.025 0.000
∆yInd
−20.058 0.029 0.051
∆yInd
−30.114∗∗ 0.026 0.000
∆yInd
−4+ ∆yInd
−50.038∗0.018 0.037
∆yInd
−6+ ∆yInd
−7−0.050∗∗ 0.018 0.007
∆wInd
−1+ ∆wInd
−4−0.047∗0.018 0.014
∆wInd
−2−0.094∗∗ 0.025 0.000
∆wInd
−3+ ∆wInd
−5-0.029 0.016 0.08
T=82(1982:(3)-2002(4)), σ= 0.22%, Portmanteau(6)=3.15, Normality :χ2(2) = 3.0
AR :F(6,54) = 1.70, ARCH :F(6,62) = 1.22, Hetero :F(42,31) = 0.67
ARvec :F(54,161) = 0.85, Normalityvec :χ2(6) = 7.28, H eterovec :F(252,163) = 0.77
LR :χ2(41) = 13.93
* means significance at 5% and ** at 1%
Table 4.2.2: The quarterly growth of Industrial employment in Belgium.
reported at the bottom of the table. Recursive estimation also confirms the absence
of a structural break in the relationships. Once again, we note from Table 4.2.2
that an increase in the growth rate of industrial output has a positive long-term
effect on employment growth in the sector. And an increased growth rate in
17lI nd is the (logarithm of the) level of wage-earning employees in the industrial sector, yI nd
is the sector’s real value-added and wI nd is real wages per person in the sector. We should
mention that we also tried GDP as the income variable for this section, but the results were not
interesting.
9
sectoral real wages has the opposite effect and leads in the long-run to reduced
employment growth.
Figure 4.2 shows the good fit of the estimated industrial employment equation.
The upper part shows actual and fitted values, and the lower section the scaled
residuals. In this case, all residuals remain within two estimated standard errors
and confirm the absence of any outliers. Comparing Figure 4.2 with Figure 4.1
shows clearly that the growth rate of employment in Industry has essentially been
negative in the period considered. This was already noted in Table 2.1.
1985 1990 1995 2000
−1.5
−0.5
0.5
1.5 Dl−Ind Fitted
1985 1990 1995 2000
−2
0
2
scaled residuals:Dl−Ind
Figure 4.2: The quarterly growth of Industrial employment in Belgium.
Once again, we can analyse the effects that a shock on one of the variables in
the system would have on the behaviour of all the variables in the long-run. The
accumulated impulse response functions are shown in the appendix. A close look
at Figure A.2.b shows that an increase in the growth rate of output in the indus-
trial sector would result over time in a similar increase in industrial employment
growth. The effect on real wages in the sector will also be positive but of a much
smaller magnitude than for employment. The positive effect on wages in Industry
is however much more clear than at the national level. The most important part
of the response to the shock becomes apparent after six quarters, so considerably
faster than at the national level. As for a one-time increase in the growth of sec-
toral wages, we can see in Figure A.2.c that the effect is a decline in the growth of
employment, but of a much smaller magnitude compared to the initial shock. The
response of employment in industry to a wage shock is also smaller than at the
national level. Such a shock also has a very small negative effect on the growth
10
of sectoral output, which unlike the situation at the national level, is insignificant
compared to the effect of increased sectoral output on sectoral wages. It is also
worth noting that the long-term effects of a shock to sectoral wages take about
twelve quarters to become apparent.
4.3 Employment in Services
In this section, we repeat the same exercise to analyse employment in Services.
Unlike the industrial sector which experienced a steady decline in employment
during the whole of the period analysed, employment in Services has seen a steady
increase in the same period. Once again, it is of interest to see if employment
behaves differently in this sector compared to the national level. The relationship
to real sectoral wages is of particular interest.
Estimating the unconstrained reduced form of the model here involves the vari-
ables ∆lSer , ∆yS er and ∆wSer.18 Johansen’s tests confirm the stationarity of the
system and the results are reported in Table 4.3.1:
rank Trace test[Prob] Max test[Prob] Trace test(T-nm) Max test(T-nm)
0 46.49[0.000]∗∗ 26.90[0.005]∗∗ 36.28[0.007]∗∗ 20.99[0.051]
1 19.59[0.010]∗13.13[0.074] 15.29[0.052]∗10.25[0.20]
2 6.46[0.011]∗6.46[0.011]∗5.04[0.025]∗5.04[0.025]∗
* means significance at 5% and ** at 1%
Table 4.3.1: Johansen’s tests for cointegration, in Services.
The following table shows the results of estimating the model by maximum like-
lihood and simplifying as far as possible. Once again, the misspecification tests
are reported at the bottom of the table. There is some possible autocorrelation
remaining in the errors of the employment equation. Normality is also rejected
both for the employment equation and for the system as a whole. But a close look
at the residuals (Figure 4.3) show the presence of one outlying observation for the
employment equation in the Service sector, occurring in the last quarter of 1987.
This could well explain why normality is rejected for this equation. A similar ouly-
ing observation exists in the wage equation for this sector in the last quarter of
1991. The combination of the two probably explains why normality is also rejected
for the system. No structural breaks are detected when doing recursive estimation
and looking at the recursive Chow-test statistics at the 1% significance level.
18These variables have the same definitions as for the Industrial sector.
11
Coefficient Std error p-value
Constant 0.077 0.070 0.28
∆lSer
−10.71∗∗ 0.10 0.000
∆lSer
−2−∆lSer
−3−0.44∗∗ 0.10 0.000
∆lSer
−4+ ∆lSer
−6−0.24∗∗ 0.09 0.009
∆lSer
−50.42∗∗ 0.12 0.001
∆ySer
−1+ ∆ySer
−20.083∗0.037 0.028
∆ySer
−4−0.120∗0.056 0.036
∆ySer
−50.09 0.054 0.091
∆wSer
−2-0.044 0.027 0.102
∆wSer
−6−0.066∗0.027 0.019
T=82(1982:(3)-2002(4)), σ= 0.33%, Portmanteau(6)=4.33, Normality :χ2(2) = 9.23∗∗
AR :F(6,57) = 3.16∗∗ ,ARCH :F(6,62) = 0.62, H etero :F(36,37) = 0.82
ARvec :F(54,161) = 0.74, Normalityv ec :χ2(6) = 28.78∗∗,Heterovec :F(216,198) = 0.80
LR :χ2(33) = 8.77
* means significance at 5% and ** at 1%
Table 4.3.2: The quarterly growth of employment in Services in Belgium.
As is clear from Table 4.3.2, an increased growth rate of value-added in this sector
has a long-term positive effect on employment growth. And an increased growth
in real sectoral wages has the opposite effect in the long-run.
1985 1990 1995 2000
−1.5
−0.5
0.5
1.5 Dl_Ser Fitted
1985 1990 1995 2000
−2
0
2
scaled residuals: Dl−Ser
Figure 4.3: The quarterly growth of employment in Services in Belgium.
Figure 4.3 above sheds more light on the behaviour of employment in Services. As
before, the upper part shows how the estimated values compare with the actual
12
values. And the lower part shows the residuals for the employment equation. The
fit of the equation is good, although the outlying nature of the observation in the
last quarter of 1987 is evident. It is also worth noting that the standard error of
the equation is larger than both the national and the Industry equations.
Comparing Figure 4.3 with Figure 4.1 shows clearly that as for employment at
the national level, employment growth in Services has been essentially positive
throughout the period considered. In fact, the mean rate of employment growth
in Services has been significantly greater than employment in general. It is worth
noting however that this growth rate has slowed down towards the end of the
sample period.
Figure A.3 in the appendix summarises the effect that a shock on one of the vari-
ables in the system would have on the others. We can see from Figure A.3.b that
an increased growth of the sectoral output has no sizeable effect on employment
in services over time. The effect of the shock on the growth of sectoral real wages
is positive but small, although larger than at the national level. The full responses
become apparent after eight quarters. If we now look at an increased growth rate
of real sectoral wages as shown in Figure A.3.c, this has a negative effect on em-
ployment in the sector. This was also the case in Industry as well as the national
level. But the response in Services is much smaller than in the other two cases.
The effect of such a shock on the sectoral output is almost insignificant in the long
term.
4.4 Stationary Equilibrium
We finish this section by using the results in Tables 4.1.2, 4.2.2 and 4.3.2 to calcu-
late what would be the relationship between employment growth, output growth
and the growth of real wages in a stationary equilibrium. The results are sum-
marised in Table 4.4.1. The difference with the impulse responses is that here
these effects are calculated from the employment equation only and therefore do
not take into account the possible feedback effects from changes in employment on
the other variables, nor the possible feedback effects of changes of output growth
on the growth of wages or vice versa.
To begin with, we can see clearly that output growth does indeed have a positive
long-term effect on employment growth at all levels. For example, a permanent
1% increase in output growth nationally leads in the long-term to an increase
in employment growth of 0.86%, excluding other feedback effects. We also notice
clearly the differences at the sectoral level. The impact on employment in Industry
is about twice that in Services. In addition, we also observe the negative effect of
an increase in the growth of wages on employment growth. The largest effect is
felt in Industry, and the smallest is in Services. Even if the result in Table 4.4.1
cannot be compared directly with the impulse response analysis, it is worth noting
that the impulse response analysis also show a smaller impact of a wage shock on
employment in the Service sector compared to Industry. It is found however that
13
the largest response was at the national level.
Sectoral Level Maximal lag Output Wages
National 7 0.86 -0.43
Industry 7 0.78 -0.72
Services 6 0.37 -0.28
The second column simply states the maximal lag
of any variable in the employment equation.
Table 4.4.1: Long-term effects of output and wage growth on employment growth:
1982:III-2002:IV.
5 Forecasts of employment trends
As a final exercise, we use the estimated employment equation at the national
level, to see what it forecasts as trends in employment over a four year period, the
lifetime of a legislature. We therefore simulate the model under specific scenarios,
whereby we impose a given growth rate of output and of wages. These scenarios
are completely fictitious and only serve to illustrate what the estimated model
suggests are the impact of these variables on employment. It should also be added
that the simulations reported below do not allow for any feedback effects between
variables, given that we impose the growth profile of both output and wages. They
are therefore to be treated with caution and only be seen as providing a sensitivity
analysis within the framework of a theoretical scenario. In particular, it would
not be appropriate to compare the simulated profiles with the actual employment
levels observed over the period 2003-2007.19
Table 5 summarises the results of three different simulated scenarios. The first
scenario (A) is one where it is assumed that over the four year projection period,
output is growing at its potential rate, which in the case of Belgium is of the order
of 0.5% per quarter. In this scenario, wages are assumed to be growing at their
average level for the period 1980-2002, i.e. the estimation period. The second
scenario (B) retains the same assumption for wages, but assumes now that output
grows at a faster rate, namely 0.7% per quarter over the whole of the period of
19It is of course possible to imagine simulating the model using the actual values of growth
in output and wages to view the resulting employment profile. However, given the disparity
between the data set we have used to estimate the model and the actual data available for the
later period, our estimated model may not quite correspond to the new data set. We cannot test
for this possible structural shift, given the small size of the new series.
14
projection. Finally, scenario (C) lets output grow at its potential level, but now
assumes complete wage moderation, i.e. a freeze on the movement of real wages.
As expected, we note that job creation is much improved when output growth is
higher than normal: keeping wage increases at the same level, our model suggests
that when output grows at the slightly higher rate of 0.7% rather than 0.5% per
quarter, then over a period of four years we can expect an increase in the net
creation of jobs of the order of 50%. We also see that for a given rate of growth
of output, wage moderation (in this case a freeze) does help to increase net job
creation by about 30% over the same period.
Scenario Output growth Real Wage growth Net number of jobs
created over 4 years
A0.5% 0.33% 62000
B0.7% 0.33% 96000
C0.5% 0.% 85000
Table 5: Simulating the model: 2003:I-2006:IV.
6 Conclusions
Our primary objective in this paper was to understand the dynamic relationship
between three fundamental variables in Belgium: economic activity measured by
the GDP , employment and wages. Despite the limitations imposed upon us due to
the lack of a reliable and long historical data set, we have nevertheless shown that
there exists a close relationship between growth and employment. We have also
shown that employment growth is related to the movement of wage costs. What
we cannot analyse is the distinction between changes in wage costs resulting from
changes in working hours or from changes in hourly wages.
Our analysis shows that increased output growth can be expected to lead to in-
creased growth of employment in general. This effect is quite insignificant in the
service sector, but it is of the same order of magnitude when it comes to Industry
or at the national level. We also find that increased output growth leads to an
increased growth in wages which is less significant at the national level than at the
sectoral level. These effects take between 1.5 to 2.5 years to take their full effect.
Our analysis also shows that an increased real wage growth generally leads to lower
employment growth. Once again though, the effect in the service sector is almost
insignificant. It is also less important in the Industry sector than at the national
level, where the effect tends to be of the same order of magnitude. These effects
take about 5 years to complete at the national level, much longer than the 3 years
15
it takes in Industry. We also find that an increased real wage growth can lead to
a downward pressure on output growth in Industry and at the national level, but
seems to have little effect on output growth in services.
Finally, we reconfirm these results in a simple exercise of post-sample forecasting
of employment levels under certain scenarios. At given wage levels, job creation
is much improved with higher growth. Similarly, at given growth rates of output,
many more jobs can be expected to be created when wage moderation is exercised.
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17
Appendix
0 10 20 30 40 50 60 70 80
−1
0
1
2cum Dl (sigmaDl=0.18)
0 10 20 30 40 50 60 70 80
−1
0
1
2
cum Dy (sigmaDl=0.18)
0 10 20 30 40 50 60 70 80
−1
0
1
2
cum Dw (sigmaDl=0.18)
a: Innovation in employment growth.
0 10 20 30 40 50 60 70 80
0
1
2
cum Dl (sigmaDy=0.64)
0 10 20 30 40 50 60 70 80
0
1
2cum Dy (sigmaDy=0.64)
0 10 20 30 40 50 60 70 80
0
1
2cum Dw (sigmaDy=0.64)
b: Innovation in GDP growth.
0 10 20 30 40 50 60 70 80
0
1
2
cum Dl (sigmaDw=0.82)
0 10 20 30 40 50 60 70 80
0
1
2
cum Dy(sigmaDw=0.82)
0 10 20 30 40 50 60 70 80
0
1
2cum Dw (sigmaDw=0.82)
c: Innovation in wages.
Figure A.1: Long-term adjustments to shocks in the quarterly growth rates of
employment, GDP and real wages.
18
0 10 20 30 40 50 60 70 80
−1
0
1
2
cum Dl_Ind (sigmaDl_Ind=0.22)
0 10 20 30 40 50 60 70 80
−1
0
1
2
cum Dy_Ind (sigmaDl_Ind=0.22)
0 10 20 30 40 50 60 70 80
−1
0
1
2
cum Dw_Ind (sigmaDl_Ind=0.22)
a: Innovation in industrial employment growth.
0 10 20 30 40 50 60 70 80
−1
0
1
2
cum Dl_Ind (sigmaDy_Ind=1.12)
0 10 20 30 40 50 60 70 80
−1
0
1
2
cum Dy_Ind (sigmaDy_Ind=1.12))
0 10 20 30 40 50 60 70 80
−1
0
1
2
cum Dw_Ind (sigmaDy_Ind=1.12)
b: Innovation in the growth of industrial value-added.
0 10 20 30 40 50 60 70 80
−1
0
1
2
cum Dl_Ind (sigmaDw_Ind=1.08)
0 10 20 30 40 50 60 70 80
−1
0
1
2cum Dy__Ind (sigmaDw_Ind=1.08)
0 10 20 30 40 50 60 70 80
−1
0
1
2cum Dw__Ind (sigmaDw_Ind=1.08)
c: Innovation in the growth of industrial wages.
Figure A.2: Long-term adjustments to shocks in the quarterly growth rates of
employment, value-added and real wages in Industry.
19
0 10 20 30 40 50 60 70 80
−1
0
1
2
cum Dl_Ser (sigmaDl_Ser=0.33)
0 10 20 30 40 50 60 70 80
−1
0
1
2cum Dy_Ser (sigmaDl_Ser=0.33)
0 10 20 30 40 50 60 70 80
−1
0
1
2cum Dw_Ser (sigmaDl_Ser=0.33)
a: Innovation in employment growth in Services.
0 10 20 30 40 50 60 70 80
−1
0
1
2
cum Dl_Ser (sigmaDy_Ser=0.62)
0 10 20 30 40 50 60 70 80
−1
0
1
2cum Dy_Ser (sigmaDy_Ser=0.62)
0 10 20 30 40 50 60 70 80
−1
0
1
2cum Dw_Ser (sigmaDy_Ser=0.62)
b: Innovation in the growth of value-added in Services.
0 10 20 30 40 50 60 70 80
−1
0
1
2cum Dl_Ser (sigmaDw_Ser=1.37)
0 10 20 30 40 50 60 70 80
−1
0
1
2
cum Dy_Ser (sigmaDw_Ser=1.37)
0 10 20 30 40 50 60 70 80
−1
0
1
2
cum Dw_Ser (sigmaDw_Ser=1.37)
c: Innovation in the growth of wages in Services.
Figure A.3: Long-term adjustments to shocks in the quarterly growth rates of
employment, value-added and real wages in Services.
20
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