MENTORING AND DIVERSITY: The Infinite Horizon Problem 2

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Proposition 3 shows that, just as in the single-period problem, the firm may prefer either homogeneity or diversity even if attention is limited to concave mentoring functions. If SCV holds everywhere, then the greater impact of additional minority managers on future mentoring always offsets the greater importance of effective mentoring of the majority pool. Then the firm benefits from increases in diversity (i.e. m closer to 1/2 ), which translates into a promotion bias in favor of the minority. Conversely, if SCV holds nowhere, then the greater importance of effective majority mentoring always dominates, the firm prefers a more homogeneous management (i.e. m closer to 0 or to 1) and the promotion bias is in favor of the majority.
There are, of course, parameter values for which SCV holds in some regions but not others. For these mentoring functions it is possible that the firm biases in favor of the majority for some values of m and in favor of the minority for others. Consider the following example: = га11, х(в) = 1 — в, and r = .3.
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MENTORING AND DIVERSITY: The Infinite Horizon Problem

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In this section, we show that our characterization of firm’s bias when it lives only two periods extends to the case where the firm faces an infinite horizon, so long as the firm’s one-period value function, 7rUB(m), is monotonic throughout the region.
Proposition 3 Consider m > 1/2. (i) Suppose that SCV holds everywhere. Then the value of the firm is increasing with the level of diversity (dV/dm < 0) and the optimal promotion policy is biased in favor of the minority (b{m) >0). (ii) Now suppose that SCV holds nowhere. Then the value of the firm is increasing as the upper level becomes more homogeneous (dV/dm > 0) and the optimal promotion policy is biased in favor of the majority (b(m) <0) comments
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MENTORING AND DIVERSITY: Characterizing Sufficient Concavity 3

Finally, we will introduce a parameter 7, which describes the scarcity of initial ability. An increase in 7 makes x steeper, so that for z > x(z; 7) — x(r — z\ 7) is non decreasing in 7. Thus, for any given promotion rule which deviates from equal proportions in promotion, then the higher is 7, the larger is the cost in terms of initial ability of the unbalanced promotion decision. Observe that our assumptions are satisfied for a linear initial ability function х(в; 7) = к — 7в. Industries where scarcity is important include industries which require specialized skills and experience, such as high-level management, or industries where “stars” are important, such as academics.
The following proposition summarizes the effects of these parameters on the condition SCV, which holds if //(m) — т^м'(1 — m) ^ 0.
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MENTORING AND DIVERSITY: Characterizing Sufficient Concavity 2

A third possibility for the shape of the mentoring function is what we call a critical mass mentoring function, which is first convex and then concave. This mentoring function incorporates the idea that fi(m) increases slowly at first due to the relative ineffectiveness of mentors who are themselves in the minority. However, the returns to additional mentors increase rapidly in the neighborhood of a “critical mass” of mentors. Once the critical mass is achieved, diminishing returns set in. For such mentoring functions, we expect that SCV will hold in some regions but not others.
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MENTORING AND DIVERSITY: Characterizing Sufficient Concavity

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We have shown that condition SCV determines the first-period promotion bias for a firm which lives two periods. Throughout the rest of the paper, we will show that condition SCV is useful in characterizing promotion biases and long-run dynamics for infinitely-lived firms. Thus, we pause to further characterize and explore this condition.
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MENTORING AND DIVERSITY: The Optimal Promotion Policy

We begin our analysis of the model by examining whether the firm’s optimal promotion policy is biased in favor of minority-type workers or majority-type workers. As a building block, we first characterize the effect of diversity on the profit of a firm which lives for only one period. The one-period model highlights the trade-off between maximizing the mentoring gain for one of the applicant pools, and exploiting the scarce initial talent in both pools.

The One Period Problem

Consider a firm which lives for only one period (i.e. w6496-8
Increasing the initial proportion of type A workers leads to an increase of //(m) in the mentoring received by the zUB type A workers who will be promoted, as well as a corresponding reduction of //(1 — m) experienced by the r — zUB workers who will be promoted. Thus, the sign of ditUB (m) /dm depends on the curvature of the fi function as well as the relative proportions of type A and В workers promoted. If the mentoring function is concave, then /x'(l — m) > and increases in diversity (i.e. a lower m) increase the mentoring of minority employees more than they decrease the mentoring of majority hires. However, since the mentoring function is nondecreasing, majority types gain more from mentoring than minority types, and the unbiased firm hires more of the (majority) A types than the (minority) В types (zUB > rj2 > r — zUB)\ thus, profits are more sensitive to the mentoring of A types than В types.

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MENTORING AND DIVERSITY: Interpretations 2

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Further, using our definition, bias summarizes a firm’s underlying preferences towards diversity; a firm with a positive bias also sees long-run profits increasing in diversity, while a firm with a negative bias sees profits decreasing with diversity. Moreover, a firm whose profits are increasing with diversity will not only bias promotion decisions, but it will also consider the impact of a broad range of actions which might advance or hinder the careers of minority managers. For example, a firm which under our definition biases in favor of the majority may also allow a “locker room” culture that discourages minority types, while a firm that biases in favor of the minority may also hire a diversity manager.
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MENTORING AND DIVERSITY: Interpretations

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We simply need to reconsider the justification for our assumptions about the surplus received by the firm for each worker. As in the ILM interpretation, surplus in the ELM model may be justified by labor market frictions or match-specific abilities. We can assume that the firm anticipates the mentoring that will be recieved by new hires.

We might also consider the case where workers of the same type are identical in terms of the value they provide to the firm, but the wage that the firm must pay to workers of a given type is increasing in the number of workers hired of each type. That is, the supply curve for each type of worker is upward sloping, so that hiring only one type of worker will increase the firm’s average labor costs. This interpretation is more appropriate for labor markets in which individuals are easily substitutable in the firm’s production function.
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MENTORING AND DIVERSITY: The Model 3

This myopic promotion policy ignores the dynamic consequences of promoting a given type and simply maximizes the current period payoff. We can now define the bias in the firm’s optimal promotion policy as
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A positive bias b(m) > 0 is then a bias in favor of type B, so that the contribution of the least qualified type A that is promoted is greater than the contribution of the least qualified type В who is promoted.
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MENTORING AND DIVERSITY: The Model 2

A worker’s type and initial ability are observable. Each applicant gains additional management skills through mentoring, represented by the function /i(-), which depends on the proportion of managers which match an employee’s type,11 though not the ability of these managers. This mentoring function is assumed to be increasing and continuous. The overall (lifetime) contribution to the firm’s profit from promoting an applicant, which we will refer to as the applicant’s “surplus,” is the following function of her type, her index and the composition of the firm when she is promoted:

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