THE ECONOMETRICS OF MACROECONOMIC MODELLING
Do NAWRU fluctuations match up with structural changes in wage formation?
We have estimated equilibrium correction wage equations:
Awct = во - ві(wc - q - a)t-i - вои + вхХг + £wt, (6.48)
which are similar to, for example, Nymoen (1989a). The results are for the manufacturing sectors of each country, and draw on the analysis of Nymoen and Rpdseth (2003). For Norway, the variables have been defined in earlier sections (see Section 4.6), and the data set contains the same variables for the other countries: wc = log of hourly wage cost in manufacturing; q = log of the index of value added prices; a = log of value added labour productivity; u = log of the rate of unemployment.[49] The terms exXt should be viewed as composite, containing both growth rate variables, for example, the rates of change in the CPI, and variables that capture the impact of changes in policy or in the institutional set-up, as in equation (6.3) of the theoretical model. Finally, A is the difference operator and ewt is a disturbance term.
Table 6.2 shows that wage growth in Norway is found to depend negatively on the lagged wage share and of the level of open unemployment, and positively on the replacement ratio variable, rprt-1. The model is dynamically homogeneous, since the elasticities of the changes in the consumer and product price indices (Apt and Aqt) sum to unity (a test of this restriction yields F(1, 21) = 0.03, which is insignificant). Another empirically valid restriction is that the elasticities of growth in product prices and productivity are equal. Thus wage-setting adjusts to changes in value added, irrespective of whether the change originates in price or in productivity. As discussed earlier (Section 4.6) the hours-variable (Aht) picks up the direct wage compensation in connection with reductions in the length of the working day.
Table 6.2
Nordic manufacturing wage equations
Norway
A(wct - pt_i) = -0.0584+ 0.446 {0.5A2(q + a)t - Apt_i}- 0.276Aht (0.007) (0.037) (0.01)
- 0.0286 ut + 0.109 Almpt - 0.2183 (wct_i - qt-1 - at-1) (0.0023) (0.017) (0.025)
+ 0.075 rprt_ 1 + 0.039 *67t - 0.054 IPt (0.013) (0.007) (0.005)
Method: OLS T = 31[1964-1994], R2 = 0.98, a = 0.58%
fEqCM = -8.8 Stab,(1) = 0.07{0.5} Staba ,(9) = 1.24{2.54}
x2ormaiity(2) = 0.19[0.901] FAR(i_i) = 2.03[0.17] Fhet,2 = 0.55[0.84]
Sweden
A(wt - pt_i) = -0.157+ 0.360 {A(q + a)t - Apt_i}- 0.849 Aht_i (0.028) (0.066) (0.338)
- 0.042 ut_i - 0.273 (wct_i - qt_i - a_i)
(0.007) (0.043)
Method: OLS T = 30[1964-1994], R2 = 0.854, a = 1.49%
f EqCM = -6.4 Stab, (1) = 0.18{0.5} Stab^,ff(6) = 0.71{1.7}
x2ormaiity(2) = 0.01[0.99] Far(i_i) = 0.04[0.84] Fhet,^ = 0.43[0.87]
Finland
A(wc - p)t = 0.110 + 0.111 rprt - 0.070 Afut - 0.008 ut-i (0.017) (0.015) (0.009) (0.003)
- 0.146 (wct_i - qt_2 - at_2)
(0.033) t t t
Method: OLS T = 33[1962-1994], R2 = 0.809, a = 1.17%
fEqCM = -4.49 Stab,(1) = 0.24{0.5} Staba ,(6) = 0.76{1.7}
x2ormaiity(2) = 0.36[0.84] Far(i_i) = 0.57[0.46] Fhet,2 = 0.50[0.84]
Denmark
A(wc - p)t = -0.032 - 0.644 A2ht + 0.428 A(q + a - p)t - 0.0322 u^i (0.022) (0.231) (0.097) (0.006)
- 0.336 (wct - qt - at_2) + 0.150 rprt_i (0.087) (0.058)
Method: OLS T = 27[1968-1994], R2 = 0.85, a = 1.51%
fEqCM = -3.88 Stab,(1) = 0.29[0.5] Stab(a ,)(7) = 0.86[1.9]
x2ormaiity(2) = 2.15[0.34] FAR(1_1) = 3.53[0.08] Fhetx^ (10,10) = 0.79[0.64]
The estimated coefficient of the variable Almpt indicates that the active use of programmes in order to contain open unemployment reduces wage pressure— Imp being the log of the share of open unemployment in total unemployment.15 Finally, there are two dummy variables in the Norwegian equation, already explained in Section 4.6: IPt and i67t.
Below the equation we report the estimation method (ordinary least squares, OLS), the sample length T, the squared multiple correlation coefficient R2, and the percentage residual standard error a. tEqCM is the t-value of the coefficient of the lagged wage share and is used here as a direct test of the hypothesis of no cointegration; see Kremers et al. (1992). Compared to the relevant critical values in MacKinnon (1991, table 1) tEqCM = —8.8 gives formal support for cointegration between the wage-share, the rate of unemployment, and the replacement ratio. This conclusion is supported by the results of multivariate cointegration methods (see Bardsen and Nymoen 2003).
Together with the standard tests of fit and of residual properties (defined in Section 4.6), we also report two of Hansen’s (1992) statistics of parameter non-constancy: StabT (1) tests the stability of the residual standard error (a) individually. Stabgj(T(10) tests the joint stability of a and the set regression coefficients (в). The degrees of freedom are in parentheses, and, since the distributions are non-standard, the 5% critical values are reported in curly brackets. Neither of the statistics are significant, which indicates that the empirical wage equation is stable over the sample.
The equation for the other countries in Table 6.2 have several features in common with the Norwegian model: dynamic homogeneity, strong effects of consumer price growth, and of pay compensation for reductions of the length of the working week.
The Swedish equation contains only two levels variables, the rate of unemployment and the wage share. Unlike Norway, there is no effect of the replacement ratio; adding rprt and rprt-1 to the equation yields F(2, 23) = 1.1, with a p-value of 0.36, for the joint null hypothesis of both coefficients being equal to zero. The insignificance of StabT(1) and StabTj^(6) indicates that the equation is stable over the sample period. We also tested the impact of intervention dummies that have been designed to capture the potential effects of the following episodes of active incomes policy and exchange-rate regime changes—see Calmfors and Forslund (1991) and Forslund and Risager (1994) (i. e. a ‘Post devaluation dummy’: 1983-85; Incomes policy: 1974-76 and 1985; Devaluation/decentralised bargaining: 1983-90). None of the associated dummies came close to statistical significance when added to the Swedish equation in Table 6.2.
The Danish and Finnish equations contain three levels variables; the replacement ratio, the unemployment rate, and the lagged wage share. In the [50]
Finnish model, the estimated coefficient of the lagged rate of unemployment is seen to be economically rather insignificant, while the change in the rate of total unemployment (Atut) has a much stronger effect. Both these features are consistent with previous findings; cf. Calmfors and Nymoen (1990) and Nymoen (1992).
The four wage equations are thus seen to be congruent with the available data evidence. We have also checked the robustness of the models, by testing the significance of potential ‘omitted variables’, for example, the levels and the changes in the average income tax rates, and a composite ‘wedge’ term, without finding any predictive power of these variables; see Holden and Nymoen (2002).
Figure 6.3 confirms the stability of the equations already suggested by the insignificance of the StabCT and StabCTj^ statistics. The first column shows the 1-step residuals with ±2 residual standard errors, ±2se in the graphs. The second column contains the estimated elasticities of the wage share, with ±2 estimated coefficient standard errors, denoted в and ±2a in the graphs. All graphs show a high degree of stability, which stands in contrast to the instability of the NAWRU estimates.
The stability of the empirical wage equations does not preclude a shift in the wage curve in the employment—real wage space, that is, if other explanatory
Figure 6.3. Recursive stability of Nordic wage equations
variables have changed. The question is whether changes in the explanatory variables of the wage equation amount to anything like the movement of the NAWRUs. To investigate this, we construct a new variable, the Average Wage - Share rate of Unemployment (AWSU). This variable is defined as the rate of unemployment that (according to our estimated wage equations) in each year would have resulted in a constant wage-share in that year, if the actual lagged wage share were equal to the sample mean.
To clarify the calculation and interpretation of AWSU, consider a ‘representative’ estimated wage equation
A(wct - pt) = во - P(wc - q - a) - fout + взД(д + a - p)t (6.49)
+ вx Xt,
where (wc - q - a) is the sample mean of the wage share, and we recognise dynamic price homogeneity, a wage scope variable with estimated elasticity вз and f3xXt which contains other, country-specific effects. Solving for ut with A(wc - q - a)t =0 imposed yields
Ut = в (wc - q - a) + —1 A(q - p + a)t + вхXt (6.50)
в2 в2 в2 в2
and the exponential of the left-hand side of (6.50) is the AWSU. In the calculations of the AWSU, actual values are used for all the variables appearing in the estimated equations. Increased upward wage pressure (due to other factors than lower unemployment and lower lagged wage share) leads to a rise in the AWSU, because to keep the wage share constant the rate of unemployment must be higher.
The graphs of the AWSU for Denmark, Norway, and Sweden are displayed in Figure 6.4. Finland is omitted, because the very low estimated coefficient of lagged unemployment implies that the mapping of wage pressure into unemployment is of little informative value. In the case of Denmark, the increase in the replacement ratio in the late 1960s explains the high AWSU estimates of the 1970s. In the 1990s, a reversion of the replacement ratio, and high growth in value added per man-hours, explain why AWSU falls below the actual rate of unemployment. For Norway and Sweden the AWSUs show quite similar developments: periods when consumer price growth is rapid relative to growth in manufacturing value added per hour (the late 1970s and early 1980s), are marked by an increase in the AWSU. In the case of Norway, the replacement rate also contributes to the rise. However, the important overall conclusion to draw from the graphs is that there is little correlation between wage pressure (as measured by the AWSU) and unemployment; in particular the rise in unemployment in the early 1990s cannot be explained by a rise in wage pressure.
