Estimates for the whole sample

A first group of results for the whole sample is reported in Table 3.4, namely models with a RW or RG specification of the permanent component, while the transitory wage is assumed to be ARMA(1,1); in both cases, no time shifters are allowed, so that the whole dynamics of the covariance structure are picked up by the linear and quadratic terms in calendar time within the permanent wage and by the correlation coefficient within the transitory one.37

Parameter estimates are well determined and indicate a substantial growth of permanent wage dispersion in both cases; in particular this is in the order of 64% in the RW case and 55% for the RG specification.38 Moreover, the RG model indicates that workers with a growth rate parameter one standard deviation above the mean will experience a 24% growth of permanent wages over the sample period. A second

Specification of the RG model assumes that the time trend is common to all workers, i.e. w' j = m + f j t , experiments have also been made with individual specific tim e trends ( w £ = p i + Y / t / , with t, measured as difference from t and the first year i is observed in sample) obtaining virtually the same results as the one presented.

* This figures are computed as )( (o 2^ ( T - l ) + cr2p )/ o 2p ] - l } * * I 0 0 for the R W and as ( [ ( o 2y ( T - l ) 2+2 rrp Y (T-1)+ o 2p ) / o 2p ] - 1) * 100 for the RG model.

3. Male wage inequality dynamics: permanent changes or transitory fluctuations?

relevant fact emerging from these estimates is the positive sign of the covariance between intercepts and slopes of the RG model ( o My) which indicates divergence in permanent wage profiles over the life cycle. This supports the interpretation which was given to the negative estimate of a My in the previous Chapter, i.e. that such an outcome was an effect of the wage indexation system: the data set of the current

Chapter is less influenced by the compressionary effect of the Scala Mobile, so that

the underlying tendency of diverging wage profiles is evident also between occupations. Taking the transitory wage into account, we can notice how, differently from Chapter 2, the ARMA specification is now supported by the data also in the presence of a dynamic permanent wage, a fact probably arising from the presence of higher variation in the data set of the present Chapter, which allows identification of more flexible specifications of individual wages. Estimates of the transitory wage parameters are fairly stable across the two models, the most relevant difference being in the MA parameter which, as an effect of the introduction of a quadratic term in the permanent covariance (i.e. for the RG specification), gets nearly halved in size. A final comment is deserved by the measures of fit. The sum of squared residuals is lower for the RG model, in line with what we would expect from the fact that this model has one additional parameter; however, this doesn’t hold for the x 2 statistic, which is lower for the less parametrised RW model, suggesting that this specification provides a better description of permanent wage dynamics.

Table 3.5 reports estimates from the same specifications of the permanent and transitory wage, but including period specific time shifters on the two wage components. By comparing these results with the ones from the previous table we

3. Male wage inequality dynamics: permanent changes or transitory fluctuations?

the permanent wage get inflated by the inclusion of the loading factors. On the other hand, the loadings are smaller than one and, for the RG specification of the permanent wage, they are monotonically decreasing over time. However, this doesn’t mean that permanent wage covariance is decreasing over time, given that we have to consider the whole impact of estimated parameters, i.e. both the loadings and the dynamics within the permanent wage components as captured by o |,o ^

and .

To better assess the dynamics of covariance components, Figure 3.5 plots out the Table's predictions in terms of variance decomposition. These predictions are obtained utilising parameter’s estimates in the formulas given in (3.7) below, where Ep(wjtwis) denotes the predicted permanent covariance structure and ET(wltWiS) is the predicted transitory covariance structure, while predicted total covariance results from the sum of the two components:

E p ( w itw i s ) =

E T (Wit WjS ) = ( Z [ ; 0V t ) ( l i > sTs) E ( v v X ) (3.7)

d j = /(; = k) j = t,s k = 0.... T - 1

"0 = T0 = 1

In both cases, it can be observed how permanent variance accounts for the largest share of the level of total variance in each time period and, in parallel to the growth in total variance, the permanent variance profile is increasing over the sample period, while the transitory variance is roughly constant. The estimates underlying the figure imply that in the RW case, total variance increased by 54% from 1982 to 1995, of which 90% can be ascribed to the permanent component; corresponding figures for the RG model are 50% and 77%. Estimates of the core permanent

3. Male wage inequality dynamics: permanent changes or transitory fluctuations?

component in the two cases still point towards a context of highly persistent, if not diverging, wage dynamics, and it is probably the large and positive estimate of in the RG case which imparts the decreasing pattern to the loading factors for the permanent component, counterbalanced by the increasing transitory dispersion in

the initial years of the sample. Combining the estimates of a* and of the loading

factors, the RG model predicts a 28% growth of permanent wages over the 17 years

period for workers one standard deviation above the mean in the distribution of y .

Again, the x 2 statistic favours the RW permanent wage specification, despite having

one parameter less than the other model. Considering this fact in conjunction with the similar conclusion drawn from the previous table, it seems that the data support a picture of individual wage dynamics characterised by the high persistence of random walk processes, rather than evolving according to theoretically derived linear profiles. In any case, both the RG and RW specifications lead us to rule out the possibility of wage convergence at this stage of the analysis.

Going back now to the dynamics of transitory wage variance depicted in Figure 3 5, we can observe how the peaks characterising total variance in 1988 and 1994 are in fact a consequence of wage volatility. Transitory wage variance is increasing in the last years of the data; in particular, from 1989 to 1995, wage volatility grows by 76% in the RW case and by 59% in the RG one. Thus, apart from the peak of 1994 which, similarly to the one which can be observed in 1988, could in part arise from the higher turmoil characterising the distribution in these years and which produced dispersion at the tails (as Figure 3.1 showed), increasing volatility can be detected within the distribution in the last part of the period under investigation, a fact which accords with the higher institutional flexibility which characterises the Italian labour market over the late 1980s and the 1990s. This is also in line with the fact that, as

3. Male wage inequality dynamics: permanent changes or transitory fluctuations?

observed when commenting on Figure 3.4, frequency mobility measures tend to drop more evidently in the short than in the medium and long run over these years: wage immobility has more to do with shock persistence in this case and washes out after a few periods. By recalling the discussion of Section 1.4, this also means that while on the one hand cross-sectional inequality has a lower impact over individual life-cycles, on the other wage profiles are characterised by higher uncertainty, which could worsen workers’ welfare.

As a next step in the analysis, Table 3.6 and Figure 3.6 report results obtained by restricting the attention to the balanced sample, i.e. by discarding those wage profiles for which observations are missing in any of the years considered. By doing so, it will be possible to get a feeling of the effects of panel attrition on the models under estimation. Moreover, the selected sample will correspond to a more homogeneous group, the cases being ruled out relating to workers moving into or out from private dependent employment or the labour force, in particular workers belonging to extreme birth cohorts beginning or ending their careers. Estimation results will thus be informative of the effects of (broadly defined) job stability on the covariance of wage components.

Compared with Table 3.5, reported parameter estimates present .a smaller dispersion of initial permanent wages (oj;), which accords with the sample design; the growth parameters of the “core” permanent variance are also lower, and similar remarks apply to the parameters of the transitory wage. The covariance between intercepts and slopes of the RG model still indicates divergence of wage profiles over the life-cycle. On the other hand, the size of the loading factors rises for the permanent component, while for the transitory one this holds only over the first part of the sample period, a drop in the transitory loadings characterising the last part of

3. Male wage inequality dynamics: permanent changes or transitory fluctuations?

the data. The fitting measures suggest a higher capability of the models in capturing empirical variation, a likely consequence of the higher homogeneity characterising this sub-sample.

Figure 3.6 shows the implication of these estimates in terms of variance decomposition. First of all we can notice how the peaks of total variance in 1988 and, especially, 1994 are smoothed out. By recalling that, for the whole sample, these were symptoms of wage volatility, the finding reflects the more stable nature of the sub-sample under investigation. A relevant difference with respect to the whole sample is given by the growth of estimated total variance, which, for the interval 1982-1995 amounts at approximately 90% for both specifications of the permanent wage. As we should expect from the sample design, permanent variance plays a predominant role in shaping overall dynamics, its contribution to total variance growth being 98 and 95% for the RG and RW model respectively; thus, a higher permanent wage homogeneity at the beginning didn’t translate into higher homogeneity at the end of the period. Accordingly, we can observe how the last part of the period is characterised by a lower level of transitory variance with respect to the unbalanced case.