PRUEBAS DE CONECTIVIDAD

The documentation of transition matrices over different time horizons carried out above is of interest in it’s own right. However, the question of whether mobility is high or low is largely a subjective one. Perhaps more interesting is the question of whether

mobility rates have changed over time. Given that there have been large changes in the shape of the cross section distribution of wages, it is not unreasonable to expect that there

may have been some changes in the level of mobility within the wage distribution. Tables 4.5a-4.5d present one year transition matrices for males and females in

1977/78 and 1988/89. Looking first at the male transitions, it is apparent that fewer

individuals are concentrated on and around the diagonal of the matrix in 1977/78 than in

number of individuals remaining in the bottom decile is 40% in 1977/78 compared to 42% in 1988/89. The respective figures for the fifth and top deciles increase from 22% to 31%

and from 61% to 66%. This looks like pretty strong evidence that mobility has fallen over this period, particularly in the middle deciles of the wage distribution.

However, one has to be careful and remember that there have been changes in

attrition from the NES/JUVOS over this period, as discussed above. The number of

individuals going missing from the panel in 1977/78 is higher than in 1988/89 and part of this change is a result of changes in the sampling procedure in the NES. Nevertheless, it

is unlikely that these sampling changes in the NES can account for such large changes in the transition matrices. Figure 4.2a shows us that the gap between the LFS and NES/JUVOS in terms of the number of individuals remaining in employment over the space of a year fell from 17% in 1977 to 11% in 1989. The NES/JUVOS has become more successful at following individuals from one year to the next.

Dealing with this problem is rather difficult since I don’t have any direct

information on who the extra individuals are. As discussed above, it is likely that these

individuals are being traced now because of the introduction of direct sampling of large organisations. Some of these individuals were probably not traced before because their

earnings fell below the National Insurance threshold. However, because they are in larger firms, it is more likely that they are individuals who have changed jobs in the month before the survey and were previously untraced because their tax records had not been updated.

One can carry out an experiment to see what the transition matrix would look like

in 1988/89 if the extra individuals were not traced. One way of doing this is to reconstruct the transition matrix by removing the extra individuals in 1988/89 and

individuals are in the transition matrix. It is quite possible that they are individuals who

are more likely to be in the bottom of the wage distribution. Therefore, I have computed the change in the numbers remaining in employment between 1977/78 and 1988/89 for each decile.^ I then reconstruct the transition matrix for 1988/89 in a way that maximises

mobility by assuming that the extra individuals are ones that stay in the same decile. This

exercise is likely to overstate the level of mobility in 1988/89 since those extra individuals in the NES/JUVOS are likely to be those that change jobs more frequently and

consequently those that are more likely to move deciles. However, even taking this “worst case” scenario, one still finds a fall in mobility over this period with a greater

concentration on the diagonal of the adjusted 1988/89 transition matrix. Most notable are the increasing numbers staying in the middle deciles of the wage distribution. For example, the adjusted figures give 40.6% remaining in the bottom decile in 1988/89

compared to 40.2% in 1977/78. However, the figure for the fifth decile is 26.1% in 1988/89 compared to 21.6% in 1 9 1 7 H B , while the corresponding figures for the top

decile are 61.8% in 1988/89 and 61.1% in 1977/78.

Comparing the one year transitions for females in 1988/89 with those in 1977/78 (Tables 4.5c and 4.5d) tell a slightly different story. The proportion on and around the

diagonals has increased between 1977/78 and 1988/89, but by less than those for males.

^ The change in the proportions remaining in employment between 1977/78 and 1988/89 for decile 1 to decile 10 respectively are: 1.15, 5.71, 6.37, 5.57, 5.32, 7.61, 6.34, 5.19, 5.28 and 4.54. The extra individuds appear to be quite evenly distributed across the deciles. Surprisingly there are far fewer extra individuals in the bottom decile of the wage distribution. However, these figures may be misleading in two respects. Firstly, they take no account of the way in which the decile thresholds themselves may change if they were computed across all individuals in both years. Secondly, we saw in Figure 2a that the aggregate proportion staying in employment from one year to the next has fallen in the LFS data.

The largest increases seem to be occurring in the middle deciles of the distribution. The percentage staying in the bottom decile increases minimally from 37.7% in 1977/78 to

38.2% in 1988/89. However, the proportion in the fifth decile rises from 27.1% to 32.3% over these years and the proportion in the top increases from 57.3% to 60.4%.

However, these results should be viewed with caution because of the changes in

attrition rates in the NES. If one carries out a similar experiment to that above to try to adjust for the lower attrition in the NES in later years, it is apparent that the proportion

remaining on the diagonal of the transition matrix has fallen slightly. This suggests that mobility for females may have risen between 1977/78 and 1988/89. However, it is

important to remember that assuming all the extra individuals in the NES are immobile is likely to overstate the degree of mobility in 1988/89.

It is of interest to see if the longer run transitions have also changed over time.

Tables 4.6a to 4.6d present five year transition matrices for males and females for 1975/80 and 1984/89. These should be compared with the matrices in Tables 4.4a and 4.4b for 1989/94. Taking males first, we can see that the transition matrices have changed little between 1984/89 and 1989/94, suggesting that long run mobility has been stable over this

period. However, when we look back to 1975/80 we find a lower concentration on the diagonal for the middle deciles but the top and bottom deciles appear not to have changed

much over time. One may consider how the change in NES attrition may effect these results. The numbers leaving the NES/JUVOS after five years appears not to have

changed very much over this time period, at least for males. As such, it could be that this

longer term attrition has not changed significantly and is less of a problem for these comparisons.

between 1975/80 and 1984/89 and again up to 1989/94. In contrast to the males, this

increase has not just occurred in the middle deciles with the proportion staying in the bottom decile rising from 15% to 20% between 1975/80 and 1989/94. However, the

proportion staying in the top decile has remained quite stable. Nevertheless, it does

appear that the attrition rate has changed for these individuals. In contrast to the males,

the numbers going missing over a five year period has fallen substantially. If we carry out the same experiment as above then it could be that five year mobility has remained

constant or even risen.

All of the analysis so far has been in terms of relative earnings classes (deciles for each year). However, it is also of interest to look at transitions across absolute earnings classes to see if any different patterns emerge. Tables 4.7a - 4.7d present transition

matrices for males and females in 1977/78 and 1988/89 where the thresholds are defined as multiples of mean real earnings in 1975 (0.5, 0.75, 1, 1.25 and 1.5 times mean earnings). Transitions out of these earnings bands can now occur not just as individuals

do better relative to others, but there can be a general shift upwards as real earnings growth effects the whole distribution. The earnings mobility one gets here is both relative

and absolute. One can see that the distribution across these earnings classes is rather uneven with most individuals in the ranges 0.75-1.25 times real earnings. Notice also that the effects of real wage growth between 1977/78 and 1988/89 are apparent, with the

distribution of individuals shifting upwards.

Taking males first (Tables 4.7a and 4.7b), it is evident that there is a concentration

on the diagonals, particularly in the middle earnings bands. As may be expected, there is

an asymmetry with more individuals moving up the distribution than down, at least in the

mean 1975 real earnings) has fallen slightly from 16.9% to 16.0% between 1977/78 and 1988/89. However, this is a very small group and the proportion leaving employment is very high and has actually risen for this group. In fact, the proportion moving up the

distribution from this group has fallen from 29% to 23%. This is quite surprising

considering we are comparing the same real earnings band over ten years apart. The proportions remaining in the higher earnings bands have risen slightly, particularly so in

the top band. However, one should remember that the numbers leaving the NES have

fallen over this period and this has potential implications for comparisons across these years.

For females we see a greater shift up the distribution due to real wage growth

between 1977/78 and 1988/89 than for males. Although the number of individuals actually in the bottom two earnings classes has fallen significantly, those that are there don’t seem to find it any easier to escape in 1988/89 than they did in 1977/78. However, those that do escape seem to move further up the distribution. The proportions remaining in the next three bands have stayed about the same, but there is some evidence of more movement up the distribution from the higher earnings bands. The numbers staying in the

top band have risen but again this may be confounded by changes in attrition.

The analysis of the decile (and absolute) transition matrices has shown that there

are quite high levels of persistence in individuals wages, with limited movement within the distribution from year to year. Looking at transitions over longer time horizons, I find

higher levels of mobility, as may be expected. Comparing transition matrices from earlier time periods it appears that the degree of mobility within the distribution has fallen, with

less individuals moving decile now than before. However, there is a potential problem with this analysis. Categorising individuals into deciles is an arbitrary method of ranking.

In doing this I am throwing away information about the movement of individuals within these deciles. In addition, when making comparisons over time one has to be careful to

check the validity of comparing deciles in one time period with deciles in a later time

period. A potential problem with the analysis above is that, with the widening of the cross section distribution of wages, the decile widths have grown over the period of analysis.

That I find more people staying in each decile is perhaps unsurprising since to move from one decile to another an individual needs a proportionately larger wage change in later

periods.^ In the next section I turn to look at other methods of analysing wage mobility and study whether it has changed over time.