The Data

The aggregate time-series data cover the period 1970:1-1990:4 and were kindly provided by the Belgian National Bank.³ The disaggregate panel data for employment, wages, and sales by enterprise were obtained from a sample of 312 manufacturing firms for the period 1978-84. They were collected by the ASLK, the Belgian savings bank. The data cover 19 industries in the 9 provinces. The sample covers 190,000 blue-collar and 79,000 white-collar workers, about one third of those in manufacturing employment. The firm-level data were supplemented by industry level employment, wages, and unemployment data.

Time-Series Results

Table 1 presents direct estimates of the Blanchard and Summers (1986) insider-outsider wage equation using 84 quarterly observations from aggregate data for the period 1970:1-1990:4. This equation gives the rate of wage inflation, w — w_-1, as a function of price inflation, Δp, and employment, n, lagged once and twice. The strong insider-outsider hypothesis—under which union members care only about the utility of currently employed members—implies that wage growth depends on the change rather than on the level of employment.⁴ The estimated coefficients appear to lend support to the strong insider-outsider theory: employment lagged both once and twice is significant (although the latter only marginally), and the hypothesis that the coefficients of employment lagged once and twice are equal in magnitude and opposite in sign cannot be rejected. The second equation replaces employment lagged once and twice with the lagged change in employment; the third equation adds a time trend. The conclusions remain unchanged: in both equations the change in employment is significant.

Table 1.

Insider-Outsider Wage Equation, 1970:1-1990:4 OLS with Δw as dependent variable

^aRamsey’s RESET test is based on the square of the fitted values.

^bThe normality test is based on a test of skewness and kurtosis of residuals.

Table 1.

Insider-Outsider Wage Equation, 1970:1-1990:4 OLS with Δw as dependent variable

	Δp-1	n-1	n-2	Δn-1	T*100	DW	R2	LM(4)	Ramsey’s RESET X2(1)a	Normality X2(2)b
(1)	1.07	0.98	–0.74			1.75	0.55	29.6	1.3	79.6
	(7.95)	(2.39)	(1.75)
(2)	1.21			1.14		1.57	0.47	36.5	2.1	38.9
	(8.60)			(2.55)
(3)	0.83			1.08	–0.02	1.94	0.63	20.6	14.6	10.7
	(6.15)			(2.89)	(6.04)
OLS with Δ(w — p) as dependent variable
(4)		0.64	–0.43		–0.02	2.27	0.43	11.4	2.5	13.3
		(2.13)	(1.41)		(6.13)
(5)				0.84	–0.02	1.88	0.30	15.4	12.1	7.7
				(2.50)	(6.02)

^aRamsey’s RESET test is based on the square of the fitted values.

^bThe normality test is based on a test of skewness and kurtosis of residuals.

View Table

Table 1.

Insider-Outsider Wage Equation, 1970:1-1990:4 OLS with Δw as dependent variable

	Δp-1	n-1	n-2	Δn-1	T*100	DW	R2	LM(4)	Ramsey’s RESET X2(1)a	Normality X2(2)b
(1)	1.07	0.98	–0.74			1.75	0.55	29.6	1.3	79.6
	(7.95)	(2.39)	(1.75)
(2)	1.21			1.14		1.57	0.47	36.5	2.1	38.9
	(8.60)			(2.55)
(3)	0.83			1.08	–0.02	1.94	0.63	20.6	14.6	10.7
	(6.15)			(2.89)	(6.04)
OLS with Δ(w — p) as dependent variable
(4)		0.64	–0.43		–0.02	2.27	0.43	11.4	2.5	13.3
		(2.13)	(1.41)		(6.13)
(5)				0.84	–0.02	1.88	0.30	15.4	12.1	7.7
				(2.50)	(6.02)

^aRamsey’s RESET test is based on the square of the fitted values.

^bThe normality test is based on a test of skewness and kurtosis of residuals.

The last two wage equations in Table 1 have the change in the real wage as the dependent variable rather than the change in the nominal wage. The results again appear to support the strong insider-outsider hypothesis. However, the results in Table 1 are not conclusive evidence of the insider-outsider theory because: (1) the pure insider-outsider wage equations do not allow for a rich set of economic variables, particularly outsider variables such as the long-term unemployment rate; (2) the equations in Table 1 are all dynamic with no long-run properties; and (3) the diagnostic tests imply that the equations in Table 1 have poor econometric properties.⁵

Before turning to panel data analysis, we explore hysteresis further in the time-series context by estimating an alternative wage equation based on the bargaining model of Nickell (1987). In this model real wages depend on productivity (output per person), y - n; employer-employee social security tax and indirect tax wedges (t₁, t₂, t₃); the import price wedge, p_m — p; and unemployment. Here we separate out unemployment into short-run, SUR, and long-run, LUR, unemployment rates to test the impact of hysteresis through the duration of unemployment.

We first estimate a long-run level equation and then derive the dynamics. In our preliminary estimates, we typically found that the replacement ratio and the employers’ tax wedge were incorrectly signed. Excluding these variables gives the long-run, or co-integrating, vector reported in Table 2.⁶ All the coefficients are correctly signed and have plausible magnitudes. The equation also appears to have satisfactory long-run properties judging by the test statistics.

Table 2.

Long-Run Wage Equations, 1970:1-1990:4^a OLS estimates with w - p as dependent variable

^aIn this table w - p (the real wage); y - n (smoothed productivity); and p_m - p (the import wedge) are in logs, while t₂ (the direct tax wedge); t₃ (the indirect tax wedge); SUR (the short-term unemployment rate); and LUR (the long-term unemployment rate) are in percent.

^bDickey-Fuller test of stationarity of the residuals.

^cAugmented Dickey-Fuller test of stationarity of the residuals.

Table 2.

Long-Run Wage Equations, 1970:1-1990:4^a OLS estimates with w - p as dependent variable

C	y - n	pm - p	t2	t3	SUR	LUR
–2.96	0.83	0.14	0.01	–0.03	–0.01	0.03
(10.80)	(9.90)	(2.50)	(5.20)	(9.04)	(2.10)	(8.40)
${\overline{R}}^2=0.97$	DW = 1.40	DFb = -6.39		ADFC = -4.35

^aIn this table w - p (the real wage); y - n (smoothed productivity); and p_m - p (the import wedge) are in logs, while t₂ (the direct tax wedge); t₃ (the indirect tax wedge); SUR (the short-term unemployment rate); and LUR (the long-term unemployment rate) are in percent.

^bDickey-Fuller test of stationarity of the residuals.

^cAugmented Dickey-Fuller test of stationarity of the residuals.

View Table

Table 2.

Long-Run Wage Equations, 1970:1-1990:4^a OLS estimates with w - p as dependent variable

C	y - n	pm - p	t2	t3	SUR	LUR
–2.96	0.83	0.14	0.01	–0.03	–0.01	0.03
(10.80)	(9.90)	(2.50)	(5.20)	(9.04)	(2.10)	(8.40)
${\overline{R}}^2=0.97$	DW = 1.40	DFb = -6.39		ADFC = -4.35

^aIn this table w - p (the real wage); y - n (smoothed productivity); and p_m - p (the import wedge) are in logs, while t₂ (the direct tax wedge); t₃ (the indirect tax wedge); SUR (the short-term unemployment rate); and LUR (the long-term unemployment rate) are in percent.

^bDickey-Fuller test of stationarity of the residuals.

^cAugmented Dickey-Fuller test of stationarity of the residuals.

The coefficient on the productivity term is close to unity and the equation indicates that if the import price wedge rises, wage earners would push up the real consumption wage. The interesting coefficients are those of the short-term and long-term unemployment rates. Short-term unemployment has the expected negative impact on wages. However, this impact is rather small: if the short-term unemployment rate rose by 1 percentage point, wages would only fall by 1 percent. Furthermore, the impact of the unemployment rate is considerably diminished by the long-term unemployment rate, which has a positive impact on wages.⁷ This evidence supports the unemployment hysteresis argument based on the duration composition of unemployment.

We now turn to the dynamics of wage determination in Belgium. The existence of indexation suggests that it is proper to model real rather than nominal wages; moreover, indexation also implies that wages are backward rather than forward looking with potentially long lags (Banque Nationale de Belgique (1991)). Also, since indexation and collective bargaining were suspended in 1982 and only fully restored in 1987, it is necessary to investigate how differently wages behaved during this period relative to the rest of the sample period.

Table 3 presents our estimated dynamic model for real wages. The equation is estimated using the instrumental variable technique because the change in productivity term is a contemporaneous determinant. In addition to this variable, the model contains lagged dependent variables; changes in the tax wedge variables; the lagged residual from Table 2, res-i; and a zero-one dummy for the 1982-86 period, D.

Table 3.

Dynamic Wage Equations, 1970:4-1990:4 Instrumental variables estimation

Table 3.

Dynamic Wage Equations, 1970:4-1990:4 Instrumental variables estimation

$\begin{array}{cccc}\mathrm{\Delta }(w-p)=0.003& +0.16\mathrm{\Delta }(w-p{)}_{-3}& +0.39\mathrm{\Delta }(w-p{)}_{-4}& +0.12\mathrm{\Delta }(y-n)\\ & \left(1.9\right)& \left(4.1\right)& \left(2.0\right)\end{array}$
$\begin{array}{cccc}-0.01{\mathrm{\Delta t}}_3& -0.003{\mathrm{\Delta t}}_2& -0.011{\mathrm{res}}_{-1}& -0.01D\\ \left(3.2\right)& \left(2.1\right)& \left(2.6\right)& \left(2.6\right)\end{array}$
${\overline{R}}^2=0.55$	DW = 2.21	SEE = 0.007
LM (χ2 (4)) = 2.97		Ramsey’s χ2 (1) = 0.89
Normality χ2 = 0.83		Heteroscedasticity χ2 (1) = 2.76

View Table

Table 3.

Dynamic Wage Equations, 1970:4-1990:4 Instrumental variables estimation

$\begin{array}{cccc}\mathrm{\Delta }(w-p)=0.003& +0.16\mathrm{\Delta }(w-p{)}_{-3}& +0.39\mathrm{\Delta }(w-p{)}_{-4}& +0.12\mathrm{\Delta }(y-n)\\ & \left(1.9\right)& \left(4.1\right)& \left(2.0\right)\end{array}$
$\begin{array}{cccc}-0.01{\mathrm{\Delta t}}_3& -0.003{\mathrm{\Delta t}}_2& -0.011{\mathrm{res}}_{-1}& -0.01D\\ \left(3.2\right)& \left(2.1\right)& \left(2.6\right)& \left(2.6\right)\end{array}$
${\overline{R}}^2=0.55$	DW = 2.21	SEE = 0.007
LM (χ2 (4)) = 2.97		Ramsey’s χ2 (1) = 0.89
Normality χ2 = 0.83		Heteroscedasticity χ2 (1) = 2.76

A number of features of this model are worth noting. The suspension of indexation during 1982-86 had a significant and negative long-run impact on real wages and, as expected, the two-yearly bargaining round and the indexation system induce long lags in wage determination. In contrast to the pure insider-outsider models of Table 1, the dynamic model of Table 3 has very satisfactory diagnostics: tests for the validity of instruments, serial correlation, functional form, normality, and heteroscedasticity give very satisfactory results.

When we included the lagged change in employment on the right-hand side to test the insider-outsider hypothesis, it was insignificant (t-statistic = 0.7). The same result was obtained when including the lagged change in the level of unemployment (t-statistic = -0.5) or the lagged change in the unemployment rate (t-statistic = -0.5).

In summary, the time-series results suggest that there is unemployment hysteresis, caused mainly by the duration composition of unemployment. Furthermore, the negative impact of unemployment on wages is very moderate in Belgium in comparison with other industrial countries. However, the time-series results were not conclusive in assessing the relevance of the insider-outsider model in Belgium. Therefore, it is useful to explore this model further using micro data. In fact, since the insider-outsider model is based on wage determination at the firm level, cross-section or panel analysis can lead to a more conclusive test of the hypothesis. In the next section we use micro data and consider the wages paid by an individual firm in view of the insider variables such as firm level productivity and profitability, and outsider variables such as unemployment, in order to be able to test appropriately for the relevance of this theory to the Belgian labor market.

Firm-Level Results

We now attempt to test for the unemployment hysteresis theories by using the firm-level data set described above. These data are from a sample of 312 manufacturing firms for the period 1978-84. The data set provides us with 2,184 observations; however, since there are some gaps in a few industry-level variables, the regressions utilize about 1,520 observations.

The firm-level results are presented in Table 4. The first panel wage equation contains mainly lagged variables and is estimated using OLS. The second panel includes current employment, n, and is therefore estimated using the instrumental variables (IV) technique. All the variables are at the firm level apart from aggregate real wages (wagg), and industry-level unemployment rate (UIND). The other explanatory variables are the firm’s productivity (y — n), measured as sales per worker; and the firm’s real profit (π). To test the insider-outsider hypothesis, the OLS equation also contains employment lagged once and twice and the IV equation has current and lagged employment. All the variables apart from the industry level unemployment rate, UIND, are in logs.

A number of features of the regressions in Table 4 are worth noting. The industry-wide unemployment rate exerts downward pressure on firm-level wages even though we allow the firm’s employment to enter the regression. This is at variance with the pure insider view of wage determination. At the same time, both employment lagged once and twice (or current and lagged employment in the instrumental variable case) as well as the insider variables such as the firm’s profits and productivity, are significant. In both the OLS and the IV estimates, the hypothesis that employment lagged once and twice (current and lagged in the IV case) have equal and opposite coefficients cannot be rejected. This implies the existence of some insider power.

To test for the hysteresis effect through the duration composition of unemployment, we added the proportion of those who have been out of work for more than a year, LTU, to the equations in Table 4.⁸ The results of this exercise are presented in Table 5. The long-term unemployment variable is highly significant and positive in both the OLS and the IV estimates.

Table 4.

Wages Equation Using Firm Level Data: Observations from 312 Firms over 7 Years (1978-84)

^aPast values of n and (w — p) were used as instruments.

Table 4.

Wages Equation Using Firm Level Data: Observations from 312 Firms over 7 Years (1978-84)

OLS
$\begin{array}{cccc}w-p=0.31& +0.91(w-p{)}_{-1}& +0.05(y-n{)}_{-1}& +0.03{\pi }_{-1}\\ & \left(89.0\right)& \left(2.2\right)& \left(2.1\right)\end{array}$
$\begin{array}{cccc}-0.09{\mathrm{UIND}}_{-1}& +0.85\mathrm{wagg}& +0.05n_{-1}& -0.04n_{-2}\\ \left(4.6\right)& \left(7.6\right)& \left(5.6\right)& \left(5.1\right)\end{array}$
N = 1,520
R2 = 0.90	DW = 2.06	SEE = 0.064
Instrumental variablesa
$\begin{array}{cccc}w-p=0.32& +0.91(w-p{)}_{-1}& +0.05(y-n{)}_{-1}& +0.05{\pi }_{-1}\\ & \left(89.3\right)& \left(2.1\right)& \left(2.8\right)\end{array}$
$\begin{array}{cccc}-0.08{\mathrm{UIND}}_{-1}& +0.94\mathrm{wagg}& +0.06n& -0.05n_{-1}\\ \left(4.1\right)& \left(8.2\right)& \left(2.4\right)& \left(2.1\right)\end{array}$
N = 1,520
R2 = 0.90	DW = 2.08	SEE = 0.064

^aPast values of n and (w — p) were used as instruments.

View Table

Table 4.

Wages Equation Using Firm Level Data: Observations from 312 Firms over 7 Years (1978-84)

OLS
$\begin{array}{cccc}w-p=0.31& +0.91(w-p{)}_{-1}& +0.05(y-n{)}_{-1}& +0.03{\pi }_{-1}\\ & \left(89.0\right)& \left(2.2\right)& \left(2.1\right)\end{array}$
$\begin{array}{cccc}-0.09{\mathrm{UIND}}_{-1}& +0.85\mathrm{wagg}& +0.05n_{-1}& -0.04n_{-2}\\ \left(4.6\right)& \left(7.6\right)& \left(5.6\right)& \left(5.1\right)\end{array}$
N = 1,520
R2 = 0.90	DW = 2.06	SEE = 0.064
Instrumental variablesa
$\begin{array}{cccc}w-p=0.32& +0.91(w-p{)}_{-1}& +0.05(y-n{)}_{-1}& +0.05{\pi }_{-1}\\ & \left(89.3\right)& \left(2.1\right)& \left(2.8\right)\end{array}$
$\begin{array}{cccc}-0.08{\mathrm{UIND}}_{-1}& +0.94\mathrm{wagg}& +0.06n& -0.05n_{-1}\\ \left(4.1\right)& \left(8.2\right)& \left(2.4\right)& \left(2.1\right)\end{array}$
N = 1,520
R2 = 0.90	DW = 2.08	SEE = 0.064

^aPast values of n and (w — p) were used as instruments.

A number of variations on the results presented in Tables 4 and 5 were also attempted. Instead of aggregate wages, we included industry-level wages. This variable was highly significant and the results remained unchanged but the diagnostics were not as good as those in Tables 4 and 5. When we substituted the aggregate unemployment rate for the industry-level unemployment rate, the results remained identical except for the coefficient of the aggregate unemployment rate, which was much lower (-0.01, t-statistic = 4.3). Since our data spanned only seven years, we chose to keep the industry-level variable, which provides more variation over the data set. Finally, the long-term unemployment variable was highly significant and positive in every single regression that we estimated regardless of the method of estimation or the other variables included.

Table 5.

Wage Equation Using Firm-Level Data: Observations from 312 Firms over 7 Years (1978-84)

(including the long-term unemployment variable)

^aPast values of n and (w — p) were used as instruments.

Table 5.

Wage Equation Using Firm-Level Data: Observations from 312 Firms over 7 Years (1978-84)

(including the long-term unemployment variable)

OLS
$\begin{array}{cccc}w-p=0.31& +0.91(w-p{)}_{-1}& +0.05(y-n)& +0.03{\pi }_{-1}\\ & \left(89.4\right)& \left(2.2\right)& \left(2.1\right)\end{array}$
$\begin{array}{cccc}-0.09{\mathrm{UIND}}_{-1}& +{0.05n}_{-1}& -0.04n_{-2}& +0.23\mathrm{LTU}\mathrm{.}\\ \left(4.7\right)& \left(5.9\right)& \left(5.1\right)& \left(7.4\right)\end{array}$
N = 1,520
R2 = 0.90	DW = 2.06	SEE = 0.064
Instrumental Variablesa
$\begin{array}{cccc}w-p=0.32& +0.91(w-p{)}_{-1}& +0.05{(y-n)}_{-1}& +0.04{\pi }_{-1}\\ & \left(89.2\right)& \left(2.5\right)& \left(2.8\right)\end{array}$
$\begin{array}{cccc}-0.08{\mathrm{UIND}}_{-1}& +0.06n& -0.05n_{-1}& +0.27\mathrm{LTU}\mathrm{.}\\ \left(4.2\right)& \left(2.4\right)& \left(2.1\right)& \left(8.0\right)\end{array}$
N = 1,520
R2 = 0.90	DW = 2.08	SEE = 0.064

^aPast values of n and (w — p) were used as instruments.

View Table

Table 5.

Wage Equation Using Firm-Level Data: Observations from 312 Firms over 7 Years (1978-84)

(including the long-term unemployment variable)

OLS
$\begin{array}{cccc}w-p=0.31& +0.91(w-p{)}_{-1}& +0.05(y-n)& +0.03{\pi }_{-1}\\ & \left(89.4\right)& \left(2.2\right)& \left(2.1\right)\end{array}$
$\begin{array}{cccc}-0.09{\mathrm{UIND}}_{-1}& +{0.05n}_{-1}& -0.04n_{-2}& +0.23\mathrm{LTU}\mathrm{.}\\ \left(4.7\right)& \left(5.9\right)& \left(5.1\right)& \left(7.4\right)\end{array}$
N = 1,520
R2 = 0.90	DW = 2.06	SEE = 0.064
Instrumental Variablesa
$\begin{array}{cccc}w-p=0.32& +0.91(w-p{)}_{-1}& +0.05{(y-n)}_{-1}& +0.04{\pi }_{-1}\\ & \left(89.2\right)& \left(2.5\right)& \left(2.8\right)\end{array}$
$\begin{array}{cccc}-0.08{\mathrm{UIND}}_{-1}& +0.06n& -0.05n_{-1}& +0.27\mathrm{LTU}\mathrm{.}\\ \left(4.2\right)& \left(2.4\right)& \left(2.1\right)& \left(8.0\right)\end{array}$
N = 1,520
R2 = 0.90	DW = 2.08	SEE = 0.064

^aPast values of n and (w — p) were used as instruments.

In short, the firm-level investigation supports the time-series result of hysteresis occurring through the duration composition of unemployment in Belgium. Furthermore, although the results reject the strong insider-outsider hypothesis, they do indicate the existence of some insider power in wage determination.