There are conflicting lines of thought about the relationship between mobility and age. Although this assumption has been contradicted in some applications and, as a consequence, generally abandoned in the Markov literature (Blumen, Kogan, and McCarthy 1955; Bartholomew 1968; McGinnis 1968; Mayer 1972), A second prediction, which departs from the stationarity assumption, expresses mobility rate as an exponentially declining function of time, that is, P{t) = [R)lP, where P(t) is the later promotion rate at time t, P is the initial promotion rate, and R is the constant proportion at which promotion rates decline. In contrast to the assumption of a constant mobility rate, this function posits a rate which declines by a constant fraction in each successive period. For example, if the rate of decline were 50%, then in each successive age interval, promotion chances would be half of what they were before. This kind of function creates a nonlinear curve on which the initial declines are largest and successive ones progressively smaller.
This formulation has been examined by Mayer (1972) and S0rensen (1975). Using synthetic cohorts constructed from the Blau and Duncan (1967) occupational changes in a generation (OCG) data, Mayer (1972) found that the exponential-decline model explains the patterns of occupational mobility for different age groups quite well. Similarly, analyzing retrospective career histories of a national sample of men, Sorensen (1975) finds comparable declines in mobility, both in terms of occupational prestige and in terms of job moves, over the sample's first 15 years in the labor force.
A third prediction is suggested by the human capital model in economics. The human capital model posits that people acquire education and experience as "investments" in their "human capital," and that these investments have positive payoffs in the labor market.
Human capital theorists also tend to cite differences in individual rates of return on investment, which makes clear predictions difficult. This is one of the less desirable features of human capital theory and will not be considered in the present analysis. For the purposes of the present analysis, the human capital model is distinctive and makes its primary contribution in explaining the rising rates in the early years.
On the other hand, the human capital model has been applied to open labor markets (Mincer 1974) and to single organizations (Wise 1975a, 1975b), but mostly for explaining salary increases. However, salaries are not always a good indicator of status since employees can obtain higher salaries without necessarily acquiring higher status; for example, by productivity bonuses, changes in individual credentials (e.g., education), longer hours, department or job-specific pay changes, or cost-of-living adjustments. Furthermore, salary is not even necessarily a good indicator of income since compensation schemes often give employees increasing proportions of their salary in non-salary forms when they are promoted (e.g., deferred compensation, stock options, insurance, pensions, perquisites, and other fringe benefits) (see McLaughlin 1975). These practices, currently common for managers, are increasingly common for non-management employees. Consequently, in some respects, promotions may be better than salary increases as indicators of status and income changes, and analyses of the distribution of promotions may complement economic research and reach somewhat different findings.
There are only a few empirical studies of promotions in organizations; however, these too arrive at conflicting results. Dalton's study of promotion in a manufacturing plant found that ages of promotion varied enormously-nearly as much as the ages in the entire work force. Although the mean ages reported seem to me somewhat low and suggest some preference for youth, Dalton concludes that his data suggest "the absence of a pattern based on age criteria" (1951, p. 408). Dalton's view of his findings comes close to the Markov stationarity assumption.
In contrast, two other studies suggest very clear age limits for promotions. Chinoy (1955) suggests from his study of automobile workers that promotions to foreman level are not made after the age of 35. Martin and Strauss (1959) also note sharp age limits for promotions. They report that "identifiable timetables of progression exist. Individuals must have moved through the foreman ranks and be ready for middle management at latest by the time they are around 35 years of age. Otherwise they tend to remain in lower-management positions" (p. 206).
Like Mayer's and Sorensen's findings, Chinoy's and Martin and Strauss's observations predict a decline in mobility over time; however, the latter studies suggest that employers may make certain ages final cutoff points beyond which no promotions take place. Their career timetable description predicts a more precipitous mobility decline than the exponential-decline model. This view seems to have been accepted in most of the current literature on careers (Slocum 1968).
The conflicting conclusions of these studies are difficult to interpret, for the authors do not present extensive empirical analyses. Martin and Strauss do not report data on promotions by age, and their findings seem to have come from employee descriptions of promotion practices, not from analyses of actual promotions. Although employee perceptions are important in their own right, they may not be a good description of reality on the issue.8 Dalton analyzes actual promotion data; however, he reports only the mean and range of promotion ages, without any consideration of the distribution of promotions within the age range.
Although models and research findings suggest several plausible predictions, none offers much insight into the operation of organizations. The Markov, semi-Markov, and human capital models were not developed to reflect any specific processes or constraints which occur in organizations; and, as S0rensen (1977, p. 976) notes, "most of the proposals for improving the Markov model are ad hoc proposals that are not based on an explicit theory of the mobility process." On the other hand, the Dalton and Martin-Strauss findings do come from studies of organizations, but neither provides a theoretical rationale for its findings. Consequently, even if one or more of these predictions were supported, the reasons would not be clear. Actually, the shape of the curve predicted by the exponential-decline model may vary a great deal, depending on the rate of decline. If each successive promotion rate declines by 50%, and the initial level of promotions is 70%; then promotion chances become less than 1% after 6 years. In contrast, if successive promotion rates decline by only 20% starting from the same initial level, it takes 20 years for promotion chances to become less than 1%. However, in neither case would a clear cutoff point be evident as in the Martin-Strauss career-timetable model, which posits a precipitous decline to no promotions at a certain age.
First, such reports may be distorted, either because they reflect organizational norms which may conflict with actual practices, because the sampled employees have distorted perceptions owing to their vantage point, or because the sampled employees distort their reports in systematic (motivated) ways. Second, even if basically accurate, such reports may be overstated or excessively general, and actual practice may be somewhat different. Quantitative analyses of actual promotions may reveal less sharp age cutoff points than respondents report to researchers, and quantitative analyses are more suited for describing variations in the implementation of a policy for different groups of employees.
