MENTORING AND DIVERSITY: Appendix

Proof of Lemma 1: In the notation of Stokey and Lucas (1989), our one period payoff function, F(m,m’) = 7r(m,m’ — (1 — r)m) is bounded and continuous; the function Г(т) = [(1 — r)m, (1 — r)m + r], which characterizes the feasible values of the state variable in the next period, is nonempty, compact valued and continuous; and the discount rate is in (0,1). Hence their Theorem 4.6 holds for our model and the value function is unique and continuous and the policy correspondence is u.h.c. The symmetry in V and \z*{m) — rj2| follow from the symmetry of our model read.
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MENTORING AND DIVERSITY: Conclusion 2

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On a more micro level, it might be interesting to deepen our understanding of mentoring, and to consider a more general set of assumptions about mentoring. For example, we could study the incentives to build mentoring relationships. In another potential extension, we might allow the level of mentoring received by a worker to depend on the characteristics of the mentor in detail.

If the effectiveness of a mentor depends on her ability, firms would be less willing to bias promotions to achieve a desired level of diversity, since hiring less qualified workers would have future as well as current costs. If the effectiveness of a mentor depends mainly on the mentoring she herself received as an entry-level worker, then initially homogenous firms will face an additional force in favor of inertia. Finally, we might wish to model the game played among workers in the firm’s hierarchy, or more generally, the forces which affect the evolution of a firm’s corporate culture.
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MENTORING AND DIVERSITY: Conclusion

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We find that when the firm draws from a diverse applicant pool, its per-period payoff may be maximized anywhere from full diversity to full homogeneity. Thus, our model provides some insight as to why some firms adopt policies of affirmative action, while others oppose such policies Link.

We further show that under some conditions, type-based mentoring may lead to a “glass ceiling,” where minority representation reaches a stable steady state which involves less diversity than in the worker pool. Finally, we demonstrate that there may be multiple equilibria. Full diversity may be the optimal stable steady state for a firm, but it may not be optimal for a historically homogenous firm to sacrifice immediate profits to achieve full diversity.
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MENTORING AND DIVERSITY: Ex Ante Human Capital Investment 2

Endogenous human capital investment will also have implications for public policy. Our formal analysis involves optimizing behavior without externalities and hence there are no inefficiencies. Unless the social welfare function includes a taste for diversity, our results do not motivate government constraints on the hiring and promotion decisions of firms. However, the strategic interdependence between the decisions of firms and workers can lead to coordination failures.

One form of coordination failure is an inefficient level of investment by workers coupled with too little promotion of minorities by firms. In addition, one might see an inefficient concentration of minorities in only a few industries or occupations, when some of those minorities might have scarce talent for other industries. Thus, there might be a role for government intervention to increase diversity.
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MENTORING AND DIVERSITY: Ex Ante Human Capital Investment

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While the model in the previous section shows that even firms in a competitive labor market may choose a diverse entry level, this result still relies heavily on the availability and scarcity of initial ability among workers of both types. In general, we expect that the relative supply of initial ability will be endogenously determined and thus might not be symmetric review.

In particular, we expect types to sort among industries taking into account not only their innate ability in each industry, but also any differentials in wages or promotion probabilities. For example, in the model of the previous section, workers of the majority type receive a wage differential when ability is supplied symmetrically by both types. We might expect additional majority-type workers to enter and minority-type workers to exit (although asymmetric opportunities in other industries may mitigate this effect).
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MENTORING AND DIVERSITY: A Two-Firm Model 4

As in our study of the basic, model, we can build on these results to consider the implications of labor market interactions for our analysis of the optimal promotion bias of each firm in a two-period model. The labor market introduces asymmetries in the initial ability functions faced by each firm. If Дх > Д2, then the initial ability function of the A’s at firm 1 shifts up relative to the B’s, while at firm 2 it shifts down (since q{ > 1/2 > g£).

As a result, more A’s are promoted at firm 1, and fewer at firm 2, than if the entry level was fully integrated (^ = 1/2). Hence, the bias at firm 1 will tend to shift towards the majority while at firm 2 the bias will shift towards the minority, relative to the single firm case. In the special case where firms are symmetric in terms of their mentoring functions and initial conditions, we will have = q% = 1/2, and both firms will be integrated at the entry level (though type A workers will receive a wage premium). In this case, our analysis of promotion policies is identical to the single-firm case.

While it is beyond the scope of this paper to solve a fully dynamic, multi-firm model and study whether firms may converge to the single firm outcome, we offer the following result.
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MENTORING AND DIVERSITY: A Two-Firm Model 3

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Part (ii) of Proposition 10 shows that if type A is the majority in both firms, then even if one firm is nearly homogenous and the other nearly diverse, it is possible that the firms will both hire and promote some minority workers. This result may seem paradoxical because the mentoring differential varies across the firms while the wage differential is constant. However, the value of hiring a type A depends not just on the mentoring differential, but also on the probability that the lower level employee makes it into management.
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