CONCLUSIONES Y RECOMENDACIONES

The model specification in this chapter has two main differences compared to the restrictions imposed on the covariance structure of Chapter 2. Let us define our model of adjusted log-wages as :

w it = 9 ( t ) w % + h (t)w j, (3.1)

where P and T denote the permanent and transitory wage component respectively, wp and wT represent the “core" of each wage component, while g( ) and h( ) are

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

functions capturing time shifts in the covariance structure. As in Chapter 2, a specification of the core permanent wage which will be adopted here is the random growth (RG henceforth) model, which allows each observational unit to have its own wage profile and whose EWMD estimation focuses on variances and covariances of intercepts and slopes of such individual profiles over the sample:

w,? = m + y it

(3.2).35

An alternative specification which will also be analysed in this chapter allows permanent wages to follow a random walk process (RW henceforth);

wit = wit- 1 + Kit

= Pi

Pi ~ ( 0 , a ^ )

Kit ~W N(Q,a\)

(3.3)

In the RG case permanent wages are supposed to evolve along linear profiles whose second moments have implications for the theory behind observed wage dynamics. The RW model, on the other hand, is more of a purely statistical kind, and is aimed at capturing the high level of wage persistence through the unit root hypothesis. As stressed in Baker [1997], such an outcome could arise from low rates of human capital depreciation or the impact of macroeconomic conditions via implicit contracts.

' 1 Theoretical underpinnings of the model and their implications in terms of restrictions on the sign of rr^y are discussed in Chapters 1 and 2.

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

The two models generate differing restrictions on the structure of second moments, in particular, while the RG imposes a quadratic dependence of covariance elements on calendar time (see equation 2.3), the RW implies a linear trend:

E Rl/l/(w ^ w £ ) = c ^ + m in (/, s )o | (3.4)

Moreover, both the models allow for mobility of permanent wages, the RG one

through the sign of the convergence parameter (ctmy , see the discussion in Chapter

2), the RW model via the size of the white noise variance , a larger value implying

greater scope for permanent wages to be reshuffled (I borrow this expression from Baker and Solon [1998]) with respect to their lagged values.

As far as the transitory component is concerned, its specification will follow the previous Chapter by hypothesising an ARMA(1,1) in which the variance of initial conditions is modelled separately from the white noise variance (the two parameters

are indicated by oq and oj?, respectively, in the tables reporting results, while p and

0 correspond to the AR and MA parameter respectively). This specification allows transitory mobility to be analysed in that it yields estimates of transitory wage correlation.

As anticipated in the Section 3.1, a central and qualifying difference with respect to the models of Chapter 2 Is given by the specification of the time varying loading factors. These parameters are meant to capture the effect of forces which inflate-deflate the distribution of the two wage components, but leaving their ranks unaltered, thus impacting on the relative importance of the two components (and

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

hence on persistence), but not on the extent of mobility within each of them. In Chapter 2, such loadings were specified as cubic functions on calendar time; here we follow Dickens [1996] and specify them as flexible time shifters, i.e. each time period has its couple of shifters, one for each component:

wit = "fW# + Ttwf, (3.5)

where 7it and t t indicate the shifters on the permanent and transitory component respectively, with the parameters for the first period set to 1 for identification. This specification implies the following restriction on second moments:

E(witwis) = C Z ^ o d>nt ) ( ' Z Ss=Odsns)E(~w! t w^ +

Œ ,r=“c!d' T' )(X f ="ods Ts

)Eiwftwl

d j = l ( j = k) j = t,s k = 0.... 7 - 1

"0 = ^0 = 1

where the dys are dummy variables indexing the rows and columns of the covariance matrix. Following this route, changes in the relative importance of the two wage components over time can be assessed without relying on specific assumptions on the functional form of the loadings.

3.3 The data utilised

The data set utilised in this study is a panel of individual wages referring to the 1979-1995 interval which has been made available by the INPS. The target population is the same as for the previous Chapter, i.e. dependent workers from the

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

private non-agricultural sector of the economy; the available sample is a 1% random drawing of all the workers registered in the INPS archive during the period examined and born between 1928 and 1970. The data set has been built by merging the information contained in a form which refers to the worker with other information concerning the firm. On the workers side, the available information consists of the gross yearly wage (inclusive of any over-time and extraordinary compensation), year of reference, year of birth, gender, occupation and number of weeks worked. Information on the firm refers to its INPS identification code, size, geographical location and five digits industry.

The data set constitutes an unbalanced panel covering roughly 100,000 wage histories. Similarly to the sample of Chapter 2, attrition problems can potentially arise from non-random movements into and out from the data, caused by the same reasons outlined in the previous Chapter. Again, no formal control for attrition has been implemented due to the lack of instruments. However, some attention will be paid to the consequences of using the unbalanced panel instead of a balanced sample.

For the purposes of this study, I select full-time male workers employed on a regular basis born between 1930 and 1970 inclusive. Moreover, in order to improve the convergence properties of the GMM estimator, I also exclude the top and bottom 5 observations from each tail of the cross-sectional distributions. This yields an unbalanced panel where the total number of wage histories is 70,002 and whose structure is reported in Table 3.1, where diagonal elements give the cross-sectional dimension of the data and extra-diagonal element are the number of observations used in the estimation of the corresponding element of the covariance matrix.

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

The cross-sectional composition of the data with respect to some workers’ characteristics is reported in Table 3.2. As can be seen, the cohort structure of the data reflects the entry of younger cohorts into the labour market; cohort turnover thus attenuates the progressive ageing of the sample with calendar time. We can also note a movement away from manual occupations, which can either reflect occupational mobility of older cohorts and a higher propensity of younger cohorts to be employed in non-manual jobs. A slight shift away from larger firms can be also observed, while the industrial structure tends to stay constant over time.

In order to construct the wage covariance matrix, the logarithms of real weekly wages (1995 prices) have first been adjusted for year, age and cohort effects. This has been done by regressing the 17 pooled cross-sections on a set of cohort dummies fully interacted with a quadratic in age and year dummies. The three effects are meant to capture business-cycle, life-cycle and productivity growth effects respectively, and the pooled cross-sections approach enables separate identification of age and birth cohorts. It’s worth recalling from Chapter 2 that the aim of this initial adjustment is to remove the influence of structural factors (such as earnings progressions with age) which generate inequality between groups and could drive the results as an effect of changes of these characteristics within the sample through time. Moreover, the control for birth cohorts is very important in the INPS data since it can capture fixed differences in education between cohorts, thus, at least partially, coping with the non-availability of education among explanatory variables.

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