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### About the Diversity Integration Model

While it is intuitive that private equity (PE) firms must both recruit and retain diverse talent to meet their diversity, equity and inclusion (DEI) goals, the specific outcomes necessary to meet those goals are not obvious. Here we present a standard deterministic time-series model to better understand what is required by firms to meet specified diversity goals over reasonable time horizons. The model is deliberately simple so that the mechanics driving the outputs are as clear as possible. That being said, we also discuss the important simplifying assumptions and the effects they could have in real-world scenarios.

### Primary features of the model

• We assume the firm is interested in increasing diversity in two dimensions: gender and under-represented minorities (URM). While other dimensions of diversity are also important, considering just these two keeps the model tractable for this particular exercise. An even simpler model could consider just gender or URM diversity separately, and we discuss this below.
• We track diversity as a percentage of a staff of fixed size.
• We look at diversity on an annual basis and model it into the future for an arbitrary number of years.

### Inputs to the model

• The starting and target percentages of women and URM – as one would expect, the closer the firm is to the target, the more quickly it can achieve its goal.
• The new recruiting mix for women and URM — if the firm is currently below its target, the new recruiting mix must be greater than the target for the firm to ever reach its goal.
• The retention rates for white males, women, and URM – The evolution of diversity depends critically on the relative retention rates. Low retention rates for women and URM can provide a significant drag on the ability of the firm to meet its goals. For example, even with high new recruiting rates for women and URM, relatively low retention rates can result in a firm never reaching its goals.

### Model dynamics

The evolution of diversity is calculated on a year-by-year basis assuming employees leave the firm at a fixed rate (1 – retention rate) specific to their gender and race/ethnicity. Exiting employees are then replaced at the recruiting rates assumed as inputs. In most cases, the near-term dynamics (e.g., first 5 years) capture most of the change in gender and URM percentages. Over longer time horizons, the model asymptotically approaches an equilibrium level (that might be above or below the target level). The recruitment of women and URM interact in this model. For example, as the percent of women employees increases, the number of white males leaving the firm will decline in number (even though the retention rate is constant) simply because the total number of white males is declining. This effectively lowers the rate at which new URM can be hired to replace white males. In practice, the dynamics could be more complicated, and we discuss this possibility below.

### The effects of other simplifying assumptions:

• The model assumes that the recruiting and retention rates are constant across years. For any given firm these will certainly not be constant, however it is not obvious how they might systematically and predictably vary as a function of other inputs. For example, it could be that as a firm gets closer to its target for women it becomes complacent and the recruiting rate for women declines. On the other hand, a higher percentage of women employees could be a cycle in which recruits perceive a firm commitment to diversity and recruiting rates for women increase. It would be a straightforward extension of the model to include a deterministic relationship between current percentages and recruiting rates. A similar logic applies to retention rates.
• In reality, most firms grow or shrink over time, but we do not model this because it adds complexity without providing much additional insight. For example, firms that are growing may be able to add more diverse workers more quickly, but each new employee will constitute a smaller and smaller share of total employees as the firm grows. In practice, firms with predictable growth trajectories should incorporate this information into their projections.
• Our model implicitly assumes that women don’t replace URMs, and vice versa. An extension of this model could separately consider white males, white women, URM males, and URM women. This would provide a more precise set of estimates but double the number of model inputs. As the percentages of women and URM get larger, it is more likely that this assumption has a meaningful effect on the results. Nonetheless, these will be second-order effects and generate inaccuracies on par with other model assumptions. Another option would be to model gender and URM completely separately. This would, for example, mean that hiring a woman was completely independent of whether the employee being replaced was white or URM. This simpler form of the model could suffer from oversimplifying the potential overall diversity issue facing the firm.

### Questions?

Contact Greg Brown, Executive Director, Kenan Institute of Private Enterprise; Sarah Graham Kenan Distinguished Professor of Finance, UNC Kenan-Flagler Business School

## Private EquityDiversity Integration Model

The PE industry is striving to achieve diversity, equity and inclusiveness (DEI) among all ranks in the front and back offices across both firm and portfolio. The Diversity Integration Model uses a few simple data inputs to calculate how long it will take PE leaders to achieve their diversity targets.