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workforce in each occupation, multiplied by the (1983 or 1991) proportion of blacks in that occupation; this is the across-occupation component, since it is the change in the proportion of blacks that would have occurred had the proportion of blacks within each occupation remained constant, with only the occupational structure changing. The second component is the sum over all occupations of the change in the proportion of blacks in the occupation, multiplied by the proportion of the workforce in that occupation (in 1991 or 1983);3 this is the within-occupation component, since it is the change in the proportion of blacks that would have occurred had the occupational structure remained unchanged. We carry out this analysis at the level of three-digit occupations. 4
Table 2.7 reports the results of this analysis for demographic changes by age, sex, race/ethnicity, and educational attainment. Although not strictly demographic categories, we also present these decompositions by occupational and employer tenure and reported incidence of formal training, which provide further insight into within-occupation changes in the workforce or workers' skills. The first column summarizes the demographic and other shifts over this period. The demographic shifts, of course, correspond to the figures, showing increased representation of women of prime working age, workers with higher levels of educational attainment, and minorities. The last 6 rows indicate a decreased share with low (1 year or less) occupational tenure, and an increased share with high (10 years or more) occupational tenure. With regard to employer tenure, the data reflect increased shares at both the high and the low ends. Finally, a greater proportion of workers reported formal training either to improve skills on the job or to obtain the job.
The last four columns report on the decomposition, using alternative base years. Looking first at the age and sex changes, we
The base year for the first component is the opposite of the base year for the second component; we report the calculation done both ways, although the results are qualitatively similar.
This analysis required using a cross-walk between occupational codes used in the two years, provided by the Bureau of Labor Statistics, to handle the relatively small number of changes in these codes.