BREAKING THE GLASS CEILING: SLOW PROGRESS AHEAD

Abstract

1. INTRODUCTION The glass ceiling that many women face as they attempt to move into top corporate positions has been studied extensively. The 1995 Report of the Glass Ceiling Commission cites many studies, all of which document the fact that a very small percentage of senior managers in large U.S. corporations are female. More recently, the organization Catalyst reported that in 2005 only 16.4% of the corporate officers in Fortune 500 companies were female. Using similar studies dating back to 1995, Catalyst calculated that the percentage of female corporate officers had increased by an average of only 0.82% per year from 1995 to 2005. Catalyst calculates that at this rate of increase it will take another 40 years for women to achieve parity in these positions. (1) Catalyst attributes this slow progress to three factors: (1) gender-based stereotyping, (2) the exclusion of women from informal networks, and (3) lack of role models for aspiring female managers. Although factors such as these may hamper women's progress toward parity, in this paper I will show that social change can occur very slowly, even in the absence of such barriers. Consider this scenario: imagine a representative large firm had from its inception employed only males in management positions. At a certain point of time, the firm dramatically alters its behavior and begins hiring equal numbers of male and female managers. Males and females are completely equal, with identical probabilities of retention, promotion, and exiting the firm. In this setting, how long will it take to transform this firm's once-entirely male management hierarchy into a gender-balanced management hierarchy? This question can be answered using an open Markov system, which is a common tool in manpower analysis. In this paper I derive equations that show the evolution of the gender composition of the management hierarchy over time for the setting described above. This scenario is interesting because it is the best case scenario for the advancement of women in management positions--once the firm abandons its old ways, there is no further discrimination in hiring, and no discrimination in promotion or retention. The nature of the model itself explicitly eliminates stereotyping and everything else that could conceivably hinder progress toward gender parity. The equations derived for this scenario therefore provide a lower bound for the time required to achieve gender parity. In the real world, lingering discrimination or a lack of role models may cause progress toward gender parity to be slower than what is suggested by these equations, but it is unlikely that progress will be faster. The equations I derive below show that the evolution of the gender composition of the managers depends on the retention probabilities within the firm. Previously published studies provide a range of real-world values for these probabilities. I generate 100,000 random samples of retention probabilities that fall within the ranges provided by published studies. Using this sample, I calculate the average gender composition of the management hierarchy 20, 40, and 60 years after the firm begins treating women equally. The results indicate that the slow progress toward parity reported by Catalyst is to be expected and will probably continue. However, the slow progress documented here is not the result of a glass ceiling or the exclusion of women from informal networks, for these have been explicitly eliminated. Change simply occurs slowly in such systems, even in the best case scenario. The outline of this paper is as follows: in Section II, I review open Markov systems and their convergence to a stable solution. In Section III, I consider a method to describe the path a Markov system takes as it moves from an arbitrary starting vector to its stable solution; knowing the path that the system traverses is integral to understanding how long it takes the system to move to its stable solution. …