5 Graphical analysis

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5.1 Patterns for men and women

Estimates of the three variance measures appear in Figures 1 to 3, with Figure 1 on total variance, Figure 2 on earnings instability and Figure 3 on long-run inequality. The breakdown of total variance is approximately 73% for the long-run inequality components versus 27% for the earnings instability component for both men and women on average over the interval. All three variance measures are also higher for women than they are for men. Second, the general pattern of change in total earnings variability has been driven primarily by changes in long-run earnings inequality; the increased degree of earnings instability in the mid-1980s to early 1990s for men, however, did play a secondary role in the run-up of men's total earnings variability, while for women the earnings instability effect was small, or even worked to reduce total earnings variability. Third, since total earnings variance is the sum of its permanent and transitory components, we will view it as the outcome of its two structural components and focus discussion on the latter.

The 1982-to-2000 period of interest is characterized by almost two complete business cycles that are useful in interpreting cyclical patterns in the variance series. A steep recession occurred over the first two years of our data (1982 and 1983), and this was followed by a strong recovery phase up until 1989. There was another severe recession in the 1990-to-1991 period. The ensuing recovery was uneven and the labour market recovery quite slow, however, as economic growth stalled from 1995 to 1996. Economic growth then became quite strong in the final several years of our sample period.

These cyclical patterns show up quite strongly for men. Long-run earnings inequality—the permanent component—rose most markedly from the 1986-to-1990 window to the 1991-to-1995 window, after it had declined very slightly from the 1982-to-1986 to the 1986-to-1990 windows; its continuing rise since the 1991-to-1995 window was again much more moderate. Since the 1986-to- 1990 window, though, long-run earnings inequality has continuously risen. Men's earnings instability, however, has generally trended downward—as has the average unemployment rate as well: from 11.1% in 1982 and 11.9% in 1983 to 6.8% in 2000. Only during the interval from the 1986-to-1990 window to that of 1989-to-1993 did men's earnings instability rise. Since the 1989-to- 1993 window, it has strongly trended down, again following the average unemployment rate, which peaked at 11.4% in 1993. The result has been a steady increase in total earnings variations since the 1986-to-1990 window.

For women in the labour market, the opposite patterns of long-run inequality and earnings instability components over the 1986-to-1990 to the 1991-to-1995 windows period is really quite dramatic, for the former rose by 9.0% while the latter declined by 11.6%. Since then, both components fell by 3.7% and 2.0%, respectively. For women, long-run earnings differentials appear to be strongly pro-cyclical—as was the case for men as well—while short-run earnings instability has pretty steadily declined since the 1986-to-1990 window pretty well independently of the business cycle. The result has been an inverted-U pattern in total earnings variation, with a broad rise from the windows of 1982-to-1986 to 1991-to-1995, after which the peak was followed by a strong decline.

Across all workers (men and women combined), total earnings variance troughed in the 1986-to- 1990 window and it peaked in that of 1991-to-1995—reflecting the severe recession in the early 1990s—and has since largely declined. Over the former recessionary period, the strong pro-cyclical run up in long-run earnings differentials was clearly the driving factor. But over the latter expansionary period, both permanent and transitory components operated to reinforce each other in reducing overall earnings variance.

5.2 Patterns by age

We have calculated estimates of long-run earnings inequality, total variance and earnings instability over time by age group. Due to space constraints, these graphs are relegated to a corresponding working paper. They contain a lot of detail, so we focus only on several highlights. Table 1 provides the actual numerical values of the three variance measures by age for the beginning and end sample windows of the 1982-to-2000 time frame.⁵ As can be seen, the patterns across ages of the two variance components are almost opposite. Long-run earnings inequality generally rises with age, at least for younger workers and beyond, so that it is markedly highest among the older-age group, much as one would expect from a standard on-the-job training human capital model; while earnings instability generally declines with age, at least until workers reach prime age, so that instability is markedly highest among entry-age workers, which is very much consistent with a career job-matching perspective. The pattern for total earnings variance basically reflects that of long-run earnings inequality, the larger source component of total variation.

For the middle two age groups—to which the great majority of workers belong—all three variance measures are also higher for women than they are for men. When averaged across all age groups, the three variance measures are higher by 21% to 25% in 1982-to-1986 and by 9% to 22% in the 1996-to-2000 window (with the biggest reduction in the male-female gap occurring in the long-run earnings inequality component from a differential of 25% at the beginning of the period down to 9% by the end of the period).

With the variance components moving in opposite directions according to age, it should not be surprising that the relative size of the variance components also varies markedly with age. Table 2 shows the ratio of long-run inequality to earnings instability across age groups. For both women and men, the ratio markedly rises with age, at least up to the prime age group (for men) and beyond (for women). For entry workers, the ratio is less than one and a half, while for prime age workers it is approximately three or more. That is, instability of earnings markedly declines in importance compared with long-run earnings differences among workers for prime age and older workers. The ratios of long-run inequality to earning instability for men and women as a whole have also risen quite markedly over the sample period covered, more so for men (from 2.32 to 3.16) than for women (from 2.41 to 2.87).

5.3 Changes in patterns by age

The figures in Tables 1 and 2 indicate that the variance component patterns have indeed changed over the sample period. The changes are highlighted in Figures 4 through 9, where age is measured along the horizontal axis. In each of these diagrams there are four age profiles: for the two end- period windows of 1982-to-1986 and 1996-to-2000; and for the two windows to facilitate a comparison of stages of the business cycle, the growth interval of 1986-to-1990 and the recessionary window of 1991-to-1995. The multiple age profiles can show whether the patterns of changes are steady (or monotonic) over the entire period or mixed (or cyclical) over the period.

All of the graphs show how long-run earnings inequality generally rises with age (cross-sectionally) for both men and women (Figures 6 and 9). Furthermore, the age profile for long-run inequality has generally shifted upward, so that such long-run inequality has been rising; but the up-shift has been much more marked for men than for women, has been more dramatic for the older age groups, and has been more persistent or steady among men while more mixed for women workers.

Figures 5 and 8 illustrate the U-shaped pattern of earnings instability across ages for men and the ski-jump pattern across ages for women. Here, though, the shifts in the age profiles for earnings instability have a more mixed pattern than for long-run earnings inequality. Over the entire interval, earnings instability has basically declined for prime-age workers (25 to 54) and shifted up for older workers, though the up-shift has not been steady over time.

Thirdly, Figures 4 and 7 also illustrate the J-shaped pattern of total earnings variance across ages for men and the general upward pattern across ages for women workers. The shifts over time in these age profiles for total variance essentially reflect the pattern of shifts in long-run earnings inequality. For men, there has been a big up-shift in total variance for prime-age and older workers, resulting in markedly widening earnings differentials across ages. Interestingly, while the (cross-sectional) age- earnings profile of mean earnings for men has been characterized by widening differentials arising from declining real wages among younger workers and steady (real) wages among middle-age workers, the change in the age profile of total variance of earnings has been characterized by marked up-shifts among prime-age and older workers. The distribution does not seem to have widened as much among the younger two age groups. For women, there has also been a big up-shift in the total variance of earnings among older workers, but there has been a decrease in the total variance of earnings among prime-age workers.

⁵ Using individual end years is always risky, but in this case the end windows are each five-year moving averages.