mentoring and diversity - harvard university and...mentoring and diversity bv susan athey,...

Mentoring and Diversity

Bv SUSAN ATHEY, CHRISTOPHER AVERY, AND PETER ZEMSKY*

We study how diversity evolves at a firm with entry-level and upper-level employeeswho vary in ability and "type" (gender or ethnicity). The ability of entry-levelemployees is increased by mentoring. An employee receives more mentoring whenmore upper-level employees have the same type. Optimal promotions are biased bytype, and this bias may favor either the minority or the majority. We characterizepo.ssible steady states, including a "glass ceiling," where the upper level remainsless diverse than the entry level. A firm may have multiple steady states, wherebytemporary affirmative-action policies have a long-run impact. {JEL J7I, J41, D20)

The related topics of workplace diversity and ofbiased hiring and promotion decisions engenderimpassioned discourse in contemporary Americansociety. Some complain that affirmative-actionpolicies lead firms to discriminate against whitemales. Others counter that the historic dominationof management by white males puts other groupsat a disadvantage, arguing that the underlying na-ture of the workplace inherently favors those whoare from similar backgrounds as their managers.They point to the fact that in many industries andoccupations, women and minorities have movedonly slowly into upper-level positions, despite thefact that the labor pool and tower levels of thework force have been diverse for some time.' This

* Athey: Department of Economics, Massachusetts In-stitute of Technology, 50 Memorial Drive, Cambridge. MA02142; Avery: Kennedy School of Govemment, HarvardUniversily, Cambridge, MA 02138; Zemsky; INSEAD,Boulevard de Constance, Fountainbleau Cedex 77305,France. We thank three anonymous referees for insightfulcomments, which greatly improved the paper. We are alsograteful to Jim Baron, Jeremy Bulow. Peter Diamond,Joshua Gans. Ed Lazear, Michael Kremer. Bill Lovejoy,Meg Meyer. Bob Marshall, John Roberts, Scott Stem, BohWilson, and seminar participants at Oxford, Stanford, andYale Universities for helpful discussions. Any errors remainour own. The authors acknowledge suppon from the StateFarm Companies Foundation and the National ScienceFoundation (Athey, SBR-9631760). Athey and Avery arealso grateful lo the Cowles Foundation at Yale for hospi-tality and support while this work was being completed.

' Large gaps exist hetween the proportion of women atlower levels and higher levels of large corporations (AnnMorrison and Mary Ann Von Glinow, 1990) and law firms(Stephen Spurr, 1990), and also to a lesser extent in aca-demic economics departments (Robin Bartlett, 1997). Inmany occupations, the 1980 Census revealed a higher pro-

phenomenon has been referred to as the ''glassceiling."

Some firms have made active efforts to reshapethemselves, instituting affirmative-action pro-grams and hiring diversity managers. For exam-ple, IBM is known for its affirmative-actionprogram, whereas American Airlines, AT&T,Colgate-Palmolive Corp., DuPont Corp., andPacific Bell have instituted diveniity programs."Other firms aggressively fight external constraintson their staffing decisions. It is difficult to recon-cile this heterogeneity among firms without spec-ifying why firms care about diversity.

This paper develops a model to analyze therelationship between the diversity of a firm'supper level and its internal promotion policies.We consider the dynamic problem faced by afirm in choosing which of its lower-level em-ployees to promote as its existing upper-levelworkers retire. Employees are characterized byan initial ability for upper-level work and by atype, which can be interpreted as gender, eth-nicity, cultural background, personality type, oreven skill set (e.g., operations versus marketingskills for managers, theorists versus empiricistsfor academics). We assume that the lower levelis split evenly between two types. We refer tothe type that has most of the upper-levelpositions as the "majority" and the other type asthe "minority."

portion of women. Blacks, and Hispanics in "employee"positions than in "supervisor" positions (Donna Rothstein,1997).

- The Walt Street Journal (August 9, 1991 p. Bl).

765

766 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 2000

Employees in our model augment their initialability by acquiring specific human capital inmentoring interactions with upper-level em-ployees. We interpret mentoring broadly, in-cluding activities such as information sharing,informal teaching, or career advice provided bymore senior workers. A critical assumption inour model is that mentoring is "type-based," inthat an entry-level employee acquires more hu-man capital from mentoring when the firm hasmore upper-level employees who match hertype.

Type-based mentoring is consistent with ev-idence from a variety of sources. Psychologistsand sociologists have documented that mentor-ing relationships within firms are more likely toform between members of the same group."*Herminia Ibarra (1992) demonstrates that thestructure of social networks depends on genderand race. More generally, communication, andthus mentoring, may be more natural and moreeffective when people share common interests(such as sports), cultural experiences, language,or when people have significant interactions in acommunity outside the workplace."* Type-basedmentoring has also been highlighted in accountsof professional partnerships. For example, a Na-tional Law Journal article^ reported.

Despite women's progress, the partner-ship ranks are 86.4 percent male. Thisputs women at a disadvantage when itcomes to mentoring, the most importantfactor in becoming a partner. Often it'sharder for women to find a mentor, be-cause the massive majority of partners aremen, and men tend to be more comfort-

' Raymond Noe (1988) and Morrison and Von Glinow(1990) review the theory and evidence in favor of type-based mentoring. More recently, George F. Dreher andTaylor H. Cox (1996) document such differences in a sur-vey of MBA graduates. Rosaheth Ranter's classic (1977)analysis of gender roles in organizations takes a similarview, observing thai "numbers—-proportional representa-tion are important not only because they symbolize thepresence or absence of discrimination hut also because theyhave real consequences for perfonnance" (p. 6).

In a related set of historical examples, Avner Greif(1993, 1994) shows that cooperation in trading relationshipscan al times be more easily sustained hetween memhers ofan extended family or community.

^ "Women's Progress Slows at Top Firms," May 6, 1996p. Al.

able mentoring other men. Rainmakingand client development—skills typicallylearned from a mentor—are keys to part-nership.^

We show that type-based mentoring hassignificant and sometimes complex effects onoptimal promotion policies and on the evolu-tion of diversity at a firm. The direct effect oftype-based mentoring is that entry-level em-ployees of the majority type acquire morehuman capital, and thus firms who base pro-motions solely on ability promote more ma-jority employees. However, since upper-leveldiversity affects a firm's profits through thementoring of future workers, the optimal pol-icy of a forward-looking firm will generallyinvolve promoting workers who do not havethe highest ability to influence the evolutionof diversity over time.

Our approach suggests that observed differ-ences in promotion decisions result from (i) tmeproductivity differences, which arise (partly) asa result of a firm's past promotion decisions,and (ii) what we call bias in promotions, that is,a decision to pass over some workers withhigher abiiity as part of a long-term plan tomove fo a desired level of diversity. Whereasmuch of the political debate abouf affirmativeaction and discrimination centers on issues offairness in the evaluation of individual workersat a given point in time, our model suggests thatthere are important efficiency considerations, aswell, in that firms can benefit from consideringtoday's promotion decisions as an investment infuture mentoring.

An important question is whether forward-looking firms benefit from increasing or

^ Similar claims have been made about the managementconsulting industry: "The lack of role models and mentorswho are black is a problem.... [t]he same issues that facehiacks in corporate America—lack of connections, lack ofmentors, and the often-present glass ceiling—face blacks inmanagement consulting" (Gautam Prakash, 1995), Simi-larly, The Wall Street Journal ("Women Make Strides, ButMen Stay Firmly in Top Company Jobs," March 29, 1994 p.Al), reponing on the effects of culture in large U.S. com-panies, argued that "as long as the percentages of malemanagers remain high, the culture remains mostly male and,women say, indifferent or hostile to their advancement.Women say they are ignored, not taken seriously ... [so]there is little chance of breaking through the glass ceiling."

VOL 90 NO. 4 ATHEY ETAL: MENTORING AND DIVERSITY 767

decreasing diversity. In our model, the oppor-tunity cost of a homogeneous upper level isan inability to take advantage of the scarcetalent of entry-level minority employees.Since minorities receive relatively little men-toring, even a minority with a very high initialability may be passed over in favor of a lessinitially able, but better mentored, majoritytype. Formally, we show that the scarcer theinitial ability {i.e., the faster the initial abilityof each type of worker diminishes in thenumber of that type promoted), the more thefirm shifts the bias toward the minority type.Consistent with this analysis, the desire toexploit the talents of an increasingly diverselabor market is often cited by firms that ac-tively promote workforce diversity,^

In general, we tind that the optimal biasneed not favor the minority, even if there aredecreasing returns to having more mentors ofa given type. Because majority employees arebetter mentored, their promotion rates can behigher than those of minorities, leading thefirm to care more about the effective mentor-ing of majority than minority employees. As aresult, a profit-maximizing firm will bias itspromotions to favor increased diversity onlyif there are sufficiently decreasing returns tomentors of a given type. The extent of de-creasing returns required to trigger a bias forthe minority depends on the scarcity of initialability, the retirement rate, and the impor-tance of mentoring.

After characterizing the optimal bias, we con-sider the effect of type-based mentoring on thelong-run level of diversity. We show that diver-sity of the upper level converges to a steadystate, which can range from full diversity tocomplete homogeneity. Our model can exhibit a

' For example, Business Week ("White, Male, and Wor-ried," January 31, 1994 pp. 50-55) reponed that to someL-ompanies, "managing diversity ... is a competitive weaponthai helps the company capitalize on its talent pool. Thegoal: to create a culture that enables all employees tocontribute their full potential to ihe company's success. Oneway is to groom more qualified women and minoritiesthrough active succession planning." Similarly, it has beenclaimed that companies use diversity programs to "attractand retain the best and the brightest ... giving a headstart inrecruiting and managing the workers of tomorrow" (USAToday. "Setting Diversity's Foundation in the BottomLine," by Del Jones, October 15, 1996 p. 4B).

glass ceiling phenomenon, whereby an initiallyhomogeneous management partially diversifies,but the "invisible barrier" of type-based men-toring stalls the progress of minorities beforethe diversity ofthe upper level mirrors the lowerlevel. Although in some cases there may be aunique long-run level of diversity, type-basedmentoring can naturally lead to multiple steady-state levels of diversity because the gains ofminorities are self-reinforcing. As minority rep-resentation increases in the upper level, thementoring disadvantage faced by new minorityemployees decreases, making it more attractiveto promote them. As a result, short-run pressureon a firm to diversify can have long-lastingimpact by moving the firm from one steady stateto another.

Our model assumes that the lower level ofthe firm is heterogeneous. This assumptionhighlights the central trade-off in the model:homogeneity increases the productivity ofmajority mentoring, but imposes an opportu-nity cost when the firm passes over scarceminority talent. This model is well suited toaddress the empirical question of why theupper levels of firms remain homogeneous,even when the lower levels are much morediverse. However, it remains to considerwhen lower-level heterogeneity is consistentwith type-based mentoring. In Section I, wediscuss a variety of (unmodeled) labor-marketfrictions that could give rise to such hetero-geneity, and in Section V we discuss an ex-tension of the model in which lower-leveldiversity is an equilibrium outcome.

Our paper differs from previous theoreticalwork on discrimination (e.g., Kenneth Arrow,1973; Stephen Coate and Glenn Loury, 1992;Bradford Cornell and Ivo Welch, 1996; AsaRosen, 1997) in several ways. First, priorwork is best suited for understanding discrim-ination in hiring rather than in promotiondecisions. For example, the assumptions ofincomplete or asymmetric information aboutworker abilities that underlies much priorwork are less palatable when an employee hasbeen with a firm for a long period of time.Second, prior work does not consider dynam-ically optimal policies. Finally, most studiesdo not unravel the forces that lead to discrim-ination within a firm, and all prior work dealswith a one-on-one relationship between the


worker and the firm. None formalizes the ideathat the current diversity of a firm affects thecareer paths of new employees.**

An important policy implication in the re-ceived literature is that affirmative-action poli-cies can actually impede the progress ofminorities by reinforcing beliefs that minoritiesare less qualified (Coate and Loury, 1992).Here, we show that affirmative action may in-crease diversity in the long run by inducing thefirm to shift from one steady-state level of di-versity to another. It is important to recognize,however, that our formal analysis involves op-timizing behavior without externalities, andhence there are no inefficiencies. Unless thesocial welfare function includes a taste for di-versity, our results do not motivate govemmentconstraints on the promotion decisions of firms,such as the short-run pressure for diversity justdescribed. Of course, there are a variety ofreasons that a society might care about the di-versity of firms. For example, the firms or theagents responsible for promotions might dis-count the future excessively, perhaps as a resultof agency problems. Further, as we discuss inSection VI, firms may not internalize the effectof their promotion decisions on the incentives ofworkers to acquire human capital.'

The paper proceeds as follows. We introduceand discuss the formal model in Section I. Sec-tion II characterizes when the optimal bias fa-vors diversity or homogeneity. Section IIIanalyzes how diversity evolves over time. Sec-tion IV discusses the empirical implications ofthe model and provides comparative statics re-sults. Sections V and VI discuss two extensionsto the model: a labor market for entry-level

^ Con.sider, for example, Cornell and Welch (1996) whostudy "screening discrimination" where employers are bet-ter able to evaluate the abilities of job applicants of the sametype as themselves. Their theory depends on unceriaintyaboul ability^ their firm consi.sts of a single employer and asingle worker; and they do not consider forward-lookingtiiring policies where firms hire minorities today so as tobetter screen them in the future.

'' Yet another potential source of inefficiencies is thatsuccessful members of a type (i.e.. individuals who attainupper-level positions) may serve as "role models" foryounger members of their community. This role modelingwould be very much like our broad definition of mentoring,except that the human-capital transfers would happen out-side of the tirm and hence v /ould not be incorporated intofirm decision making.

employees, and ex ante human capital acquisi-tion. Sectioti VII concludes.

I. The Model

A single firm employs a continuum of upper-level and lower-level employees.'^ We normal-ize the measure of upper-level employees to 1.There are two types of employees, labeled Aand B. The proportion of upper-level employeesof type A in period t is denoted m'. In eachperiod a proportion r E (0. I] of the upper-level employees retire and must be replaced.Retirement rates are uniform, meaning that rm'workers of type A and r( I - m') workers oftype B retire in period /. We will typically treatA as the majority and B as the minority in ourexposition (i.e., m' ^ V2).

The firm operates an internal labor market inwhich retiring employees are replaced from thelower level, which has an equal number of A'sand B's. With this assumption we introduce acost of upper-level homogeneity, which we be-lieve to be quite general: homogeneous firmsbear the opportunity cost of passing over tal-ented workers of the opposite type within theirorganization. There are numerous reasons whythe lower levels of organizations are diversedespite type-based mentoring (which introducesa benefit to segregating entry levels by type).For example, firms generally differ in their lo-cations, cultures, and skill requirements, andthus workers may have firm-specific prefer-ences and skills that make it beneficial for adiverse group of employees to work at the samefirm. Search costs might reinforce the effects offirm-worker matching. Further, in the present le-gal and political environment, a variety of non-market forces create pressure for diverse lowerlevels." Finally, as discus.sed in Section V, partialdiversity of the lower level can arise in equilib-rium even without labor-market frictions.

'"In our 1994 Stanford GSB working paper (Athey etal., 1994) we consider a model of type-based mentoringwith a finite number of employees where initial ability isstochastic. The qualitative insights of the stochastic modelare the same, but the deterministic model analyzed in thispaper is more tractable.

" Segregated firms may be at risk of govemment andcivil litigation for biased hiring practices. They may alsoface social pressure to mirror the composition of their locallabor markets.

VOL 90 NO. 4 ATHEY ET AL. MENTORING AND DIVERSITY 769

We assume that there are at least r entry-level workers of each type and that the twopools of lower-level workers are symmetricin their initial abilities. Member d G [0, r] ofa pool of entry-level workers has an initialability x{6), which represents the surplusgained by the firm when worker 6 takes anupper-level position.'^ The function x(6) isassumed to be nonincreasing. Thus, the qual-ity of the marginal worker from each pool(weakly) decreases as the firm digs deeperinto that pool, representing scarcity of abil-ity for upper-level work. Such scarcity maybe especially relevant for jobs in the servicesector, jobs requiring education and special-ized skills, jobs where "stars" are important(such as academics, entertainment, andsports), and high-level management positionsin firms.

A worker's type and initial ability are observedby the employer. Each entry-level employee gainsadditional (firm-specific) skills required for upper-level work through mentoring, represented by thefunction /iC), which depends on the proportion ofupper-level employees with the same type.'"^ Thismentoring function is assumed to be increasingand continuously differentiable. A promotedworker makes an overall (lifetime) contribution tothe firm's profit that depends on her type, herinitial ability, and the composition of the firmwhen she is promoted:'"*

5^(6, m) = x(e) + afx{m)

'^ There are several potential sources of such a surplus.The worker's ability might be specific to the firm-workermatch, it might not be observable by other firms, or theremight be frictions in the labor market.

' ' The effectiveness of mentoring does not depend on theability of upper-level employees. If mentoring depends lin-early on the average ability of all upper-level employees,then our analysis is unaffected. However, the analysis isaffected if mentoring depends on the average ability ofupper-level employees with the same type. We expect thatsuch dependency would reduce the magnitude of the pro-motion bias because promoting less-able candidates be-comes less attractive.

'•" These surplus functions do not include Ihe indirectcontribution from future mentoring of other workers; theseeffects are incorporated into the firm's dynamic program-ming problem that follows. Further, observe that, althoughour primary interpretation of mentoring is firm specific, anygeneral skills in mentoring may accrue to the workers. Thusthe surplus functions can be interpreted as the benefit to thefirm net of wages.

and

. m) = x(e) - m).

where a parameterizes the importance ofmentoring relative to initial ability. We de-note by z' G [0, r] the measure of the pro-moted employees in period / who are oftype A, r — z' are then of type B. The firm'sper-period profit function is the total sur-plus generated by its new upper-level em-ployees:

7r(m, z) =

+

, m) dO

ss(e, m) de.

The firm seeks to maximize the discounted sumof its per-period profits by choosing a sequenceof promotion policies (z\ z^, —) to solve thefoiiowing maximization problem:

(1) V(m) = max S 6'7r(m', z'){z'.z\-) (=0

subject to m'^' = (1 - r)m' + z',

z' £ [0, r] and m^ = m.

Given a value function (which is establishedto be well behaved for our mode! in the Appen-dix), we can define the optimal policy corre-spondence by

Z*{m) = {zB[O, r]\V(m)

= TT(m, z) + 8V(z+ (1 - r)m)}.

We are interested in how m' evolves over timeand in how the firm biases its promotions.We define the unbiased (or myopic) promotionpolicy z^^(m) implicitly from the equation


1.95

1.85.

1.75-

1.65-

1.55.

1.45

Type 5 Ability:

NumberHired

z (m)

FrouRE i. SURPLUS FUNCTIONS AND PROMOTION POLFCIES

Notes: As indicated with the horizontal line, unhiased promotions equalize final abihties across the two types. The optimalpromotion pohcy entails a bias in favor of type B. Parameters are given in Example 1 with S = 0.95.

which equalizes the contribution of the mar-ginal promoted employee of each type.'''

We can now define the bias in the firm'soptimal promotion policy as

A positive bias b(m) > 0 is then a bias in favorof type fi.'^

Given the promotion policies z'^^ and z*, wecan define transition functions M^^(m) and

" If the worst type A is better than the best lype B U^(r.m) > Sg{Q, m)] so thai ihe marginal contributions cannotbe equalized, then the firm only promotes type ^ ' s andz"''{m) = r. Similarly, if s^ir. m) > s^((i, m) thenz^^m) = 0.

'^ There are other ways to define bias in our model. Forinstance, one could define bias as any deviation from equalpromotion rates [i.e., as |;*(m) - rl2\] since the pool ofinitial ahiliiies is the same for each type. This definitionproduces more of a bias for ihe majoriiy. Alternatively, onecould define the bias as any deviation from promoting theapplicani who contrihutes the most to long-run firm profits,including ihe indirect contribution from mentoring others;ihen there is no bias. One advantage of our definition is thatit is linked to a firm's preferences about diversity. Thus afirm that biases for the minority (by our definition) wouldaiso be willing to incur other costs to facilitate minoritycareer advancement, such as hiring diversity managers.

A/*(m), which give the state achieved in periodr + 1 as a function of the period t state m:

M ^ V ) =m{l - r) + .T^V).

M*{m) = {m'\m' = (1 - r)m + z,

where z G 2*(m)}.

Figure 1 plots the surplus functions, s^{6, m)and 5B{6, m), for an example. Since type A is themajority {m = 0.9), 5 is greater than s^ by theamount of the mentoring differential, in this case^(0.9) - /x(O.I). When unbiased promotion pol-icies are used, by definition, the surplus of themarginal promoted employee is the same acrossthe worker types, so that the firm promotes mostlytype A workers, hi this example, the optimal biasis positive, so that when the optimal promotionpolicy is used, fewer type A workers are promotedthan with an unbiased promotion policy, and themarginal type A worker is better than the marginaltype B worker.

Note that it is possible to reinterpret ourmodel as applying to hiring rather than promo-tion decisions. Then the "upper level" is thefirm's whole workforce, and the "lower level" isthe pool of applicants. The key assumptions arethat the productivity of new hires depends on


the proportion of more setiior workers with thesame type and that there is a diverse applicantpool. Under this interpretation, our results char-acterize the firm's optimal hiring policy and theevolution of the diversity of the firm's entirework force.

Il, The Optimal Promotion Policy

We begin our analysis by characterizing thedirectioti of the optimal promotioti bias. As abuilding block, we first characterize the effect ofdiversity on the profit of a firm that lives for onlyone period. The one-period analysis highlights thecritical trade-off betweeti maximizing the mentor-ing gain for one of the applicant pools and exploit-ing the scarce initial talent in both pools.

The optimal policy of a firm that lives justone period (i.e., 5 = 0) is unbiased promotions[z^ (w)], since the firm does not care aboutfuture mentoritig performed by promoted work-ers. The profit of such a firm is then

7r (m) - Trim, z^'im)).

Suppressitig the dependence of z^^ on m, wecan rewrite this as follows:

+ (r - z^«)a^(l - m)

toring received by the z^" type A workers whoare promoted, as well as a corresponding reduc-tion of Q:;Lt'(l — m) for the r — z^^ type Bworkers who are promoted. Thus, the sign ofdiT^^{m)ldm depends on the cui^ature ofthe /xfunction as well as the relative proportions oftype A and B workers promoted.

If the mentoring function is concave, then/j,'(l - m) > ix'(m), and increases in diversity(i.e., decreases in m) increase the mentoring ofminority employees more than they reduce thementoring of majority employees. However,since the mentoring function is nondecreasing,majority types receive more mentoring than mi-nority types, and a myopic firm promotes moreofthe majority (A) types than the minority (B)types iz^^ > rll> r - z^^)\ thus, profits aremore sensitive to the mentoring oi A types thanB types.

As a result, the firm's profit increases withthe diversity of its upper level only if the men-toring function is concave and the degree ofconcavity is sufficient to overcome the largerweight placed on mentoring outcomes for ma-jority workers. We shall say that sufficient con-cavity (SCV) holds at m > Vz if {dl

^^im) < 0. that is, if

r -

By the envelope theorem, the effect of achange in the initial level of diversity is givenby:

(2)

Further, we say that sufficient concavity holdseverywhere {SCV everywhere) if SCV holds forall m > '/2. Similarly, we shall say that suffi-cient concavity holds nowhere {SCV nowhere)if SCV fails (with a strict inequality) for eachm > 1/2 .

Now consider a firm that lives three periods.In the second period, the bias favors the minor-ity if and only if SCV holds: SCV determineswhether having more minority workers in thefinal period increases or decreases profits in thatperiod. However, the problem for the firm in thefirst period is more subtle. A critical feature ofour setting is that

- m ) .

Increasing the initial propottion of type A work-ers leads to an increase of a/Lt'(m) in the men-

, z)dm dz

= aix'{m) + - m) > 0,


SO that in any period the returns to having moreof some type in the upper level are increasing inthe promotion probability of that type. Thiseffect reinforces the bias as we move back fromperiod 2 to period 3. Suppose that SCV holdseverywhere, so that the period 2 bias favors theminority. Since more minorities are promoted inthe second period than would be with unbiasedpromotions, the firm biases for the minority( and more so than if the hotizon were only oneperiod). Incorporating this logic into an induc-tive argument, we can show that the character-ization of the one-period profit function carriesover to our infinite-horizon model, yielding un-ambiguous predictions about the direction ofthe optimal bias.

PROPOSITION I: (i) If SCV holds every-where, then the value of the firm is increasingwith the level of diversity (dVldm < 0). andthe optimal promotion policy is biased infavor of the minority for each m. (ii) If SCVholds nowhere, then the value of the firm isincreasing as the upper level becomes morehomogeneous (dVldm > 0), and the optimalpromotion policy is biased in favor of themajority for each m.

In many settings, we expect that the mentor-ing function should exhibit decreasing returns(i.e., (X is concave). In its most literal sense,mentoring refers to a voluntary relationship be-tween a more experienced employee and a newhire. An increase in the proportion of upper-level employees of a given type may allowlower-level employees who would otherwise beunmatched to find a mentor (or a more appro-priate mentor). The first minorities in the upperlevel yield high returns by providing mentoringto those who would not otherwise have receivedit. At higher levels of diversity, additionalupper-level minorities simply provide some-what better mentoring possibilities to those whowould have been mentored anyway. This sug-gests decreasing returns to mentoring as diver-sity increases.

However, Proposition 1 shows that diminish-ing returns are not sufficient for the optimalpromotion policy to be biased in favor of theminority type. Even with decreasing returns, afirm may still bias its promotion decisions infavor of majority types, because they make up

the bulk of those promoted as a result of theiradvantage in the mentoring process. Conse-quently, our model is consistent with heteroge-neity in a firm's attitudes toward diversity evenunder decreasing returns. Section IV character-izes how SCV depends on other exogenouselements of the model, such as the scarcity oftalent and the retirement rate.

There are, of course, functional forms forwhich SCV holds in some regions but not oth-ers. Then, it is possible that the firm biases infavor of the majority for some values of m andin favor of the minority for others.

Example I: Suppose jLt(m) = m" , x(0) =1 — 6, r = 0.3, and let 8 take on one of thevalues {0, 03, 0.95}.

Figure 2 plots the one-period value function,TT^''(m), for m ^ Vi for Example 1. Note thatprofits increase with diversity except when m ^0.927. Figure 3 graphs the unbia.sed promotionrate (z!^^) for type A applicants as well as theoptimal promotion rates for S = 0.3 and S =0.95. The bias in favor of type B workers, b(m\6), is the difference between the unbiased pro-motion rate (S = 0) for type A's and the biasedpromotion rate.

Figure 3 shows that for 5 = 0.95, the firmalways biases in favor of the minority; despitethe fact that the one-period value function isincreasing near 1, the firm finds it worthwhileto bias promotions toward full diversity,which maximizes the one-period profit func-tion. In contrast, if 8 - 0.3, the firm's optimalpolicy is to bias in favor ofthe majority in theregion [0.93, 0.96], and in favor of the mi-nority elsewhere. Thus, even within a singlefirm, attitudes toward diversity will changewith the initial conditions. We further discussthe dynamics of this example in the nextsection.

Before proceeding, we pause to observe thatthe dependency of profit on diversity identifiedin Proposition I has implications not only forpromotion decisions, but also for any invest-ment decision or organizational design decisionwhose impact varies by type. For example, therelationship between diversity and profits af-fects a firm's willingness to build a strong cor-porate culture that favors the development ofthe current majority type.

VOL 90 NO. 4 ATHEY EJ AL: MENTORING AND DIVERSITY

0.5555 ^

0.555 .

0.5545 .

0.554

0.5535

773

0.5530.5 0.6 0.7 0.8 0.9

FIGURE 2. THE VALUE FUNCTION WITH UNBIASED PROMOTIONS

Note: Parameters are given in Example I with 5 = 0.

ni . The Dynamics of Diversity

We now analyze the evolution of diversity atour firm. We are interested in three questions:What is the effect of bias on the level of diver-sity? Is there a glass ceiling? To v 'hat extentdoes history matter?

We begin with some definitions. As our focusis on long-run outcomes, it is useful to define asteady-state level of diversity m^, such that themeasure of retiring A managers exactly equalsthe measure of type A's that are optimally pro-moted: rm^ G z*{m^). Figure 3 graph.s the"retirement function" R{m) = rm and the pro-motion policy z*{m) for Example 1 with 5 = 0,0.3, and 0.95. Each crossing of the retirementand promotion functions represents a steadystate. Thus, {0.5, 0.936, 1} are steady stateswhen 5 = 0.3.'^ We refer to a steady state,which is always reached from a neighborhoodsurrounding it, as a stable steady state (e.g., the

'^ Steady stales in our model are symmetric in ihat if mis a steady state, so is 1 - m. Hence, in Example 1 with 8 =0.3, the full set of steady states is (0, 0.064, 0.5, 0.936, 1}.

points {0.5, 1} when S = 0.3).'^ Let 9^* be theset of stable steady states under the optimalpromotion policy and let ^^^ be the set ofstable steady states with myopic promotions.We show in the Appendix that the level of diver-sity always converges to a stable steady state witheither optimal (biased) or unbiased promotions, sothat both 'J'^^ and ^* are nonempty.

Type-based mentoring causes the diversityof the firm to change over time in potentiallycomplex ways, even when promotions areunbiased. Hence, it is useful to decompose theeffect of type-based mentoring on the dynam-ics into its direct effect on the unbiased pro-motion rate, and its indirect effect on theoptimal bias.'^ We therefore begin with re-sults related to the stability of full diversity

'** More formally, the level of diversity m is stable for thetransition function M if there exists a f > 0 such ihal, for allV > e > 0 such that Mtm + e) and M(m - e) are singlevalued, m + e ^ (<)M(m 4- e) and m — E ^

''' Moreover, the dynamics of a myopic firm are ofinterest from a policy perspective, because they highlightthe long-run outcome when firms implement a "type-blind"promotion policy.


0 29

0.27 .

0.25 .

0,23 .

0.21 .

0.19 .

0.17 •

015 .

Retiremeni ofType ^Workers

fr<^^V^^ 095^ ^ M ™ . - 0 , 9 5 ,

0,5 0.7 0.9

0,3

0,295

0,29-1

0.285

0.28 -I

0.273

0,27 \

0,265

0.26

0.9 0,92 0,96 0,98 1Proportion ofType A Workers

FIGURE 3. THE DYNAMIC EVOLUTION OF DTVERsrrv FOR

DIFFERENT DISCOUNT FACTORS

Notes: The upper panel plots the retirement rate against theoptimal promotion policies for 5 = 0. 0.3, and 0.95. Asindicated hy the arrows in the lower panel, when the retire-ment rate is greater (less) than the promotion rate, the firmmoves toward greater (less) diversity. Parameters are givenin Example 1,

and the existence of multiple steady statesunder unbiased promotions. In general, ourmodel is consistent with an arbitrary constel-lation of stable steady states. ** With someadditional structure, however, it is possible toprovide sharper predictions.

PROPOSITION 2: With unbiased promotions:(i) Full diversity is a stable steady state if andonly if the asymmetries created by type-basedmentoring are small relative to the scarcity oftalent in the neighborhood of full diversity:Vi G V^^ O afi'('/2) < -rx'{rl2). (ii) If

^ Indeed, it can be shown that for any finite, symmetricset of points X C [0, i ], there exists a nonincreasing initialability function x and a nondecreasing mentoring function fisuch that 9'^* = X.

jLi"'(m) > 0 \/m and x(e) = K - yO. then^^^ C {0, '/2, 1},- and if u."'{m) < 0 Vm andx{e) = K - ye. then &"^^ = {m,, 1 - m Jfor some m^ ^ Vz .

We now tum to the dynamics under optimalpromotions. A final definition is useful for iden-tifying the effect of the optimal bias on theevolution of diversity.

Definition 1: Consider two sets of stable steadystates, y i and ^2- ^ ^ say that 9'i is morediverse than ^2 if

min{m|m E ^2- "^ — j)

> min{m m

max{m|m G ^2- 'n — j}

> max{m|m G 9'|,m > ^}.

PROPOSITION 3: (i) If SCV holds nowhere,then ^^^ is more diverse than S'*, and fulldiversity is never a stable steady state {V2 ^&'*). (ii) !f SCV holds everywhere, then &>* ismore diverse than &'^^ and full diversity is astable steady state if aii'{Vz) < -rx'(r/2).

What is the impact of bias on diversity? Notsurprisingly, a bias that favors the majority (aswhen SCV holds nowhere) increases long-rundiversity, whereas a bias in favor ofthe majority(as when SCV holds everywhere) decreaseslong-run diversity. As a result, public policiesthat seek to force firms to use a "type-blind"promotion policy can have ambiguous effects.

We say tfiat the firm has a glass ceiling when-ever, in the long run, the upper level is not asdiverse as the (fully diverse) lower level. FromProposition 3(i), we know that full diversity isnever a stable long-run outcome when the biasfavors the majority. Then, firms that start withhomogeneous management may diversify some-what, but the progress of minorities always stopsshort of full diversity. Conversely, when the biasfavors the minority [Proposition 3(ii)], full diver-sity is a possible long-run outcome, as long as theasymmetries created by type-based mentoring arenot too large relative to liie scarcity of talent.

To what extent does history matter for the

VOL 90 NO. 4 ATHEY ET AL: MENTORING AND DIVERSITY 775

firm? For extreme values of a there is a uniquelong-run level of diversity, whatever the histor-ically given initial conditions.

PROPOSITION 4: For a sufficiently large, theunique long-run stable steady state entails ahomogeneous upper level (^* = {0, 1 }). As aapproaches 0, each stable steady state ap-proaches '/2.^'

When mentoring is unimportant (a small),the .scarcity of talent and the uniform retirementrate pushes the firm toward full diversity. Con-versely, when mentoring is important (a large)the upper level is necessarily dominated by onetype. Then, history determines which type isdominant, but not the level of diversity.

For intermediate values of a, interior stablesteady states may arise, and more important,there may be multiple steady-state levels ofdiversity. We saw in Proposition 2(ii) that type-based mentoring may lead to multiple steadystates with unbiased promotions; multiplesteady states can arise with optimal promotionsas well, as illustrated in Example 1 with 6 =0.3. Intuitively, multiple steady states may arisebecause the level of minority advancementtends to be self-perpetuating: with few minori-ties in management, minorities are poorly men-tored and hence few are promoted.

When there are multiple steady states, short-lived pressure on a firm to diversify (e.g., fromlegislation or other forms of social pressure) canhave a long-lasting impact on the level of di-versity. When pressure pushes diversity above acritical mass point,"^ the gains of the minoritiesare self-reinforcing, even if the pressure is re-moved. Thus, history determines the level oflong-run diversity. In Example I with 8 = 0.3,a firm that starts with a homogeneous upperlevel stays there, unless it is forced to promoteenough minorities so that m' < 0.936, in whichcase convergence is to full diversity.

Our theory predicts not only that the level ofdiversity changes over time at a firm, but thatthe attitude toward diversity (i.e., the directionofthe bias) changes as well. In Example 1 with

• ' For fL concave, we have the slightly stronger resultthat ^ * = [Vi) for a sufficiently small.

" By a "critical mass point," we mean a sleady state tbalhas no basin of altraction.

8 = 0.3, a firm starting just to the left of thecritical mass point m" = 0.936 initially biasespromotions in favor of the majority. Over time,however, diversity still increases because theoptimal bias and type-based mentoring are notsufficiently strong to overcome the greater re-tirement rate of the majority type. As m' falls,the optimal bias shifts and eventually favorsminorities.^^

We close our discussion of dynamics with asecond example that uses a "critical mass" men-toring function, which is first convex and thenconcave, so that mentoring is relatively ineffec-tive until the minorities reach 30 percent of the

Example 2: /i,(m) = 0 for m ^ 0.3, ix(m) =0.15 + O.\(m - 0.3) " for m > 0.3, r =0.3, 8 = 0.3 and 4 0 ) = 1 - 0 -

Figure 4 graphs this mentoring function.^^ Inthis example, there is a glass ceiling and multi-ple steady states, even though per-period profitsare maximized at full diversity. Eigure 5 graphsthe evolution of diversity in this example froma variety of starting points. Starting from homo-geneity, minorities make some initial progressinto the firm, yet there is a glass ceiling: theynever reach a level of representation above 10percent, even if the firm starts out with close to20 percent minorities. On the other hand, ifexternal pressure pushes minorities beyond thecritical mass of 20 percent, convergence is tofull diversity. The region of increasing returnsin the critical mass mentoring function

•' Similarly, a firm starting to ihe right of m° = 0,936initially biases promotions in favor of [be majority, but ashomogeneity increa.ses and decreasing returns becomestronger, the optimal bias shifts to favor the minority.

~* This mentoring function incorporates the idea that|i(m) increases slowly at first as a result of the relativeineffectiveness of mentors who are themselves highly iso-lated in the organization. Mentoring becomes effective onlywben a critical mass of mentors is reached. Similar curva-ture could also arise if the efficiency of communication andinformation sharing rises sharply once a critical mass isreached.

" Notice that this mentoring function bas an upwardjump, which strictly speaking violates our smoothness as-sumption; however, the smoothness assumption is not nec-essary for a computational analysis, and in any event thefunction could be approximated with a differentiable func-tion.


0.3 n

0.25.

0.2 .

0.15.

0.1 .

0.05-

Mentoring ReceivedBy Type A Workers

0.4 0.6 0.8 1.2

Proportion ofType A Workers

FIGURE 4. A CRITICAL MASS MENTORING FUNCTION

Note: Parameters are given in Example 2.

Strengthens the general tendency for minoritygains to be self-perpetuating and hence for his-tory to matter.

IV. Empirical Implications of the Model

We now develop the empirical implicationsof our theory. Section IV, subsection A, identi-fies the exogenous parameters that lead firms toprefer diversity, and thus favor minority groupsin their optimal promotion policies. Section IV,subsection B, derives comparative statics forlong-run levels of diversity.

A. Factors Influencing the Promotion Bias

Section II linked a firm's attitude toward diver-sity to the curvature of the mentoring function,and more specifically to the SCV condition. Anyfactor that influences the unbiased promotion pol-icy has an impact on whether SCV holds, and thuson the sign of the optimal promotion bias. In thissection, we focus on the effects of the retirementrate r, the importance of mentoring a, and thescarcity of initial ability.

We parameterize the scarcity of initial ability

by 7, where an increase in y makes the initialability function x steeper. Formally, we assumethat x(z\ y) — x(r - z\ y) is nonincreasing in7 for 2 > r/2. Thus, the higher the 7, thegreater the cost (in terms of lower average ini-tial ability of promoted employees) of deviatingfrom the policy of promoting an equal numberof each type. T'he linear initial ability functionx(Q; y) = K - yd satisfies this requirement.

Proposition 5 identifies the effects of a, r,and 7 on both the unbiased promotion policyand on (d/dm)TT^^(m), whose sign determineswhether SCV is satisfied.

PROPOSITION 5: For m > Vi, (i) The unbi-ased promotion rate, z^^(m; a, y, r), is (a)nonincreasing in y; (b) nondecreasing in a. (ii)(d/dm)TT^^(m; a, y, r) is (a) nonincreasing iny: (b) nondecreasing in a; and (c) nonincreas-ing in r whenever x(6; y) = K — yB and 11 isconcave.

An increase in the scarcity of initial ability(7) makes it more likely that the firm biases forthe minority. As scarcity rises, it becomes morecostly to promote disproportionately from the

VOL 90 NO. 4 ATHEYETAL: MENTORING AND DIVERSITY 777

Proportion of Type A Workersin the Upper Level

Period

11 16

FIGURE 5. THE "GLASS CEILING"

21

Noies: The figure plots the state of the firm as a function of time, starting from different initial conditions. Parameters aregiven in Example 2.

majority pool. The more minorities promotedwith the unbiased policy, the more likely it isthat a myopic firm (and, by Proposition 1, aforward-looking firm) benefits from having adiverse upper level. Industries in which scarcityis important include those that require special-ized skills and experience, such as high-levelmanagement, as well as industries where "stars"are important, such as academics.

Conversely, the greater the importance ofmentoring a, the more majority employees arepromoted by a myopic firm, since their mentor-ing advantage is larger, and thus the firm is lesslikely to bias for the minority.^^ Industries inwhich mentoring is likely to be important rela-tive to initial ability include services, law, aca-demics, industries where networking and

•*• When a becomes sufficiently large, the firm's optimalpolicy will select only majority types (SCV will hold no-where): for a sufficiently close to zero, unbiased promotionselects almost the same number of majority and minoritytypes, and then the concavities of fi and SCV are (approx-imately) equivalent.

information sharing play an important role, andindustries where apprenticeships are importantcomponents of training. In contrast, mentoringwill be less important in Industries in which jobsare well defined, require few specialized skills,and involve little information sharing.

An increase in the retirement rate r has anambiguous effect on the sign of the optimalbias. As turnover increases, the firm generallypromotes more workers of both types, but long-run diversity depends on the proportion of mi-norities who are promoted. Suppose that thementoring function is concave. Then, the direc-tion of any change depends on the curvature ofthe initial ability function. When the initial abil-ity function is linear, an increase in turnoverincreases unbiased majority and minority pro-motions by the same amount. But since there isa higher marginal return to minority mentors,this change makes it relatively more attractiveto promote minorities. Industries with low turn-over at the senior level relative to the size ofthe firm might include law, academics, busi-nesses organized by partnership, and large

THE AMERICAN ECONOMIC REVIEW SEPTEMBER 2000

bureaucracies; high turnover occurs in manyhigh-technology industries, as well as intetme-diate levels of hierarchies.

B. Factors Influencing Long-RunDiversity Levels

We now explore the extent to which the com-parative statics in the previous section apply tolong-run levels of diversity. Since it may bedifficult to directly observe the direction of thepromotion bias, the results in this section maybe more useful for interpreting observed pat-tems of diversity in finns. We take a localapproach to comparative statics, in that we lookat the effect of small changes in a parameter ona given steady state.'^ Large changes in a pa-rameter can alter the set of steady states, andhence are harder to analyze. Despite the factthat the local approach is somewhat restrictive,we still find that several of our results fromProposition 5 must be qualified when applied tolong-run diversity levels.

Most of our results follow from the first-orderconditions (FOC) for an optimal promotion pol-icy at a stable steady state:

LEMMA I: For all m,, i= V2 which are stablesteady states, there is a unique optimal promo-tion policy, z*{m^). An interior steady stateffij ? {0, Vi, 1} satisfies the following first-order condition

= — TT(m,, z,)oZ

where Zs = rm^.

— (I — r) 8 dm

That is, the return to promoting more majority-type workers today is balanced against the

^ Another approach woutd be to derive comparative staticson the optimal bias, and use these results to analyze changes insteady states. However, in contrast to the sign of the optima]bias, there is no necessary connection between comparativestatics on the magnitude of the bias tiom a two-period model(which would follow from Proposition 5). and comparative staticson the magnitude of the bias in the infiniie-horizon model.

(weighted) return to having a lower level ofdiversity in the next period. Proposition 6identifies the main comparative statics results.

PROPOSITION 6: Each stable steady statem, ^ Vi is:

(i) Nonincreasing in response to a small in-crease in y.

(ii) Nonincreasing {nondecreasing) in re-sponse to a small increase in 8 when SCVholds everywhere (nowhere).

(iii) (a) Nondecreasing in response to a smallincrease in a, when SCV holds nowhere.(b) Nondecreasing in a when 6 is suffi-ciently small.

(iv) (a) Nonincreasing in response to a smallincrease in r when SCV holds everywhereand x{d) = K — yd. (b) Nonincreasing(nondecreasing) in r ifdz^^/dr < (>)m^when S is sufficiently small.

We now look at the intuition for each of thecomparative static results, as well as some ofthe implications. In developing the intuition it isuseful to note that M*(m) = M^^{m) - b(m),so that the effect of a parameter can be decom-posed into its direct effect on the unbiased dy-namics and an indirect effect resulting fromchanges in the optimal bias.

Proposition 6(i) shows that long-run diversityincreases with (small) increases in the scarcityof ability. By Proposition 5, the direct effect ofan increase in scarcity is an increase in theunbiased promotion rate for minorities. There isalso an indirect effect: when the firm anticipatespromoting more minorities in the future, it caresmore about their mentoring and hence the biasmoves toward the minority. Thus, both the di-rect and indirect effects support an increase indiversity.

Although we do not formally model asym-metries in initial ability between types, it isstraightforward to analyze asymmetries usingthis result. If the initial ability of one typebecomes less scaree, the promotion rates andbias shift in favor of that type. One implicationis that the entry of more women and minoritiesinto the workforce will cause firms to shift theiroptimal bias toward these groups. Another im-plication is that in a multilevel organization.

VOL. 90 NO. 4 ATHEY ET AL: MENTORING AND DIVERSITY 779

diversity might fall in higher levels of the hier-archy. This follows because inequities in onelevel will lead to lower promotion rates for thedisadvantaged type, and thus inequities at onelevel will be reinforced at the next-higher level.This is consistent with the evidence cited in theintroduction about the glass ceiling, as well asBartlett's (1997) description of diversity inthe economics profession.^^

Now consider the effect of changes in thediscount rate. As 5 increases, the firm is morewilling to bias promotions to improve futurementoring. Hence, the effect of a change in 5depends on the direction of the optimal bias. Ifthe bias favors the minority (majority), thendiversity increases (falls).

As an application of this result, suppose thatthe owners of the firm have a larger discountrate than do the managers who make promotiondecisions. In practice, this type of agency prob-lem might arise because managers take intoaccount the fact that they will leave the firm (orat least their current job) with positive proba-bility in the future. Then, a firm with a mentor-ing function that is SCV everywhere may havea suboptimal level of diversity. Inefficiencies ofthis kind are consistent with the observation thatmany firms have internal rules or policies thatrestrict decisions about diversity in hiring andpromotion. "^ Furthermore, since such agencyproblems may exist even in top management,shareholders may wish to constrain the deci-sions of top management about diversity.""*

-** Notice that our finding contrasts with a simple butplausible altemative theory, whereby firms use type-blindhiring policies in response to govemmeni regulation, butthen discriminate (perhaps because of a taste for discrimi-nation) in internal promotions. The altemative theory wouldpredict a sharp fall in diversity from the entry level to thenext-higher level, but relatively constant promotion ratesafter that.

""Gur theory also raises the possibilily that some firmswith agency problems might want to adopt rules that limitdiversity. We do not typically observe such rules, probablybecause of legal and social costs associated with explicitdiscrimination against minorities.

^ The ability of shareholders to dictate diversity policyhas been a topic of recent debate by the Securities andExchange Commission (SEC) (see Steven Wallman,"Equality Is More Than "Ordinary Business,' " New YorkTimes. March 30. 1997 p. 3). In 1993, the SEC reversed along-standing policy by allowing Cracker Barrel Old Coun-try Store to exclude a shareholder resolution that prohibitedjob discrimination on the basis of sexual orientation, argu-

The effect of a small increase in the importanceof mentoring can be ambiguous because the indi-rect effect can oppose the direct effect. The directeffect of an increase in a is that more majoritytypes are promoted by a myopic firm. In terms ofthe indirect effect, this will further tend to shift theoptimal bias of a forward-looking firm toward themajority. However, any increase in the importanceof mentoring also makes the firm more willing tobias promotions (in either direction) to optimizefuture mentoring. If the bias is for the majority {aswhen SCV holds nowhere), then the two indirecteffects work in the same direction, and diversityunambiguously falls with a. Similarly, if 5 issufficiently small, the optimal bias is small, andthe direct effect dominates. Since for sufficientlylarge a, SCV holds nowhere, shifts when a isalready large should unambiguously decreasediversity.

The direct effect of a change in r is alreadyambiguous, as we saw in Proposition 5. Ofcourse, for S small, the direct effect dominates.In general, increases in r make the firm morewilling to bias promotions (in either direction)since current promotions have an immediateand large effect on diversity. Thus, even whenthe initial ability function is linear (and thusfaster turnover increases the returns to minoritypromotions under the unbiased policy), unam-biguous predictions about steady states followonly when the bias favors the minority.

Although these results provide predictionsabout the link between exogenous features ofthe environment and patterns of diversity, theyalso require some qualification. First, note thatthe results for a and r require additional as-sumptions: the parameters affect both the unbi-ased promotion rates and a firm's willingness tobias promotions. On balance, though, it seemsplausible that diversity should be lower in in-dustries in which mentoring is very important,and higher in high-turnover industries (if thementoring function is sufficiently concave). Asecond issue is that, as in any model with

ing that diversity policy fell within the range of "ordinarybusiness matters," which by SEC rules cannot be dictated byshareholder resolutions. Recently, shareholder interestgroups have questioned the policy change. Our analysissuggests that shareholders may indeed have an interest indirecting company policies toward diversity, even beyondthe more widely cited issues of legal liability.


multiple steady states, it can be difficult to drawinferences from cross-sectional observations.Two firms with the same technology operatingin similar labor markets can potentially havevery different levels of diversity, depending ontheir histories. These firms might also have verydifferent attitudes toward diversity.

V. Markets for Entry-Level Workers

Our model abstracts from labor-market con-siderations to focus on the evolution of diversityat a single optimizing firm with a given level ofdiversity among its entry-level workers. In re-ality, the diversity of a firm's entry level isendogenous. An important question, then, iswhether lower-level diversity is consistent withour assumption of type-based mentoring. Ourworking paper (Athey et al., 1998) considers asimplified extension of the model to include twomyopic firms and a competitive labor market forentry-level employees. We now briefiy outlinethe main insights from this extension.

We find that there may be entry-level diver-sity when both firms have the same majoritytype, even if their existing levels of diversitymay differ. Then, both firms want to hire thesame type, but the less diverse firm is moreeffective at mentoring them. Despite this asym-metry, each firm may end up with a diverselower level, because there are decreasing re-turns to hiring the majority type. To understandthe source of decreasing returns, observe thatthe more majority workers a firm hires, themore intense the competition for promotion andthe lower the probability that any given majorityworker is promoted. Since firms are trying tomaximize the ability of promoted workers, thedeclining promotion probability for majorityworkers leads to decreasing returns. Like anyscarce resource with decreasing returns, it canbe optimal to share that resource across firms,which in our case means diverse entry levels.

Heterogeneity of firms (for example, in loca-tion, culture, or specialty) also tends to supportentry-level diversity. We find in our workingpaper that the addition of a productivity benefit( unrelated to type or ability) from matchingfirms to workers leads to even stronger results.We allow half of the workers to be more pro-ductive at firm 1 by an amount c ^ 0 (observ-able prior to the hiring decision), whereas the

other half of the workforce is more productiveat firm 2 by the same amount c. For any c > 0,we find that the entry level is fully diverse if theinitial diversity levels of the firms are suffi-ciently similar.

Of course, competition could yield segregatedoutcomes for some parameters, in parficular if themajority type differs across firms. In practice, wedo sometimes observe segregated outcomes. Con-struction companies in some U.S. cities are dom-inated by a particular ethnic group. Someacademic disciplines have large representationsfrom particular nationalities, and gender integra-tion is surprisingly heterogeneous across disci-plines, even within the sciences.

In summary, the extension suggests that theinsights of our single-firm model may he mostapplicable in industries where one type has his-torically dominated the industry and the exist-ing firms differ in some way. In such industries,if the firms start out sufficiently similar and thediscount rate is sufficiently low, our single-firmanalysis will apply to the multifirm problemwithout modification.^'

VI. Ex Ante Human-Capital Investment

From a policy perspective, it is important toconsider the interaction between human-capitalinvestment decisions and firm promotion deci-sions when there is type-based mentoring. An-ticipating poor mentoring prospects and hence alow probability of promotion even if their initialability is high, B-type workers might choose toinvest little in the specialized human capitalrequired for upper-level work. Then, invest-ments in human capital provide an additionalmechanism to sustain self-perpetuating beliefs.In many cases, we expect to find one equilib-rium where B types have a low level of invest-ment, and another equilibrium with a high levelof investment.

These low-investment equilibria could be in-

" In Athey et al. (1998), we also compare the dynamicsof the two-firm extension to those in the single-firm modelwith S = 0. We find that the stable steady states of thesingle-firm model are also symmetric steady states of thetwo-firm model, and further, for c > 0, the firms convergeto these steady states if they start out sufficiently close. Forc sufficiently small, we find that full segregation is also apossible steady state.

VOL. 90 NO. 4 ATHEY ETAL: MENTORING AND DIVERSITY 781

efficient for a variety of reasons. For example,as new workers will tend to invest in humancapital for industries in which their type hashigh representation, there could be an inefficientclustering of minorities in only a few industries,occupations, or firms, when some of those mi-norities might have been better matched else-where. In fact, such behavior has been observedhistorically, as documented in the literature on"sex segregation" (Andrea Beller, 1984; Bar-bara Bergmann, 1989). Further, if one type isthe minority across many industries or firms,that type might have very low incentives forhuman capital investment. This suggests a ra-tionale for government policy to promote diver-sity where the government seeks to coordinatethe economy on a high-investment equilibrium,perhaps by subsidizing education or training fortype B workers in certain industries.

VII. Conclusion

This paper develops a novel perspective ondiscrimination and diversity. We begin with theview that firms possess a stock of upper-tevelemployees. With type-based mentoring, the di-versity of this stock matters, since it affects theflow of payoffs from newly promoted workers.A firm faces a trade-off in its promotions be-tween homogeneity, which maximizes the men-toring of a particular type, and diversity, whichallows the firm to make use of scarce talent ofworkers of both types. The firm's promotionpolicies are thus biased, in the sense that firmssacrifice current profit to increase or decreasefuture diversity. We find that a firm's optimalbias may favor diversity or homogeneity, andthat the firm's attitude toward diversity dependson the curvature of the mentoring function, thestrength of type-based mentoring, the scarcityof talent, the rate of retirement, and the discountrate. Thus, our model provides some insight asto why some firms adopt policies of affirmativeaction, whereas others oppose such policies andeven pass over minorities who have overcomethe mentoring disadvantage.

Further, our model has implications for theevolution of diversity over time, given initialconditions. Our model can exhibit a glass ceil-ing, whereby the proportion of minorities in theupper level reaches a stable steady state, whichinvolves less diversity than at the lower level.

We also demonstrate that there may be morethan one possible long-run level of diversity ata given firm. Even if full diversity is the mostprofitable steady state for a firm, it may not beoptimal for a historically homogeneous firm tosacrifice immediate profits to achieve full diver-sity without outside pressure.

Our model is predicated on several assump-tions, notably that firms select from a lower-level workforce with talented workers of bothtypes, and that firms capture some of the surplusfrom mentoring. Our model is most likely to beapplicable for industries where firm-specific hu-man capital is important and difficult to acquirethrough formal education (so that mentoring isimportant); and where specialized or unusualskills are required and where talents vary withthe firm-worker match (so that there is hetero-geneity in the lower level). Examples that areespecially appropriate include large industrialcompanies, investment banks, academic depart-ments and professional service firms, and part-nerships including those involved in law andconsulting.

Empirical evidence about mentoring and di-versity requires data on the diversity of organi-zations, preferably over time. Unfortunately,much of the publicly available data is collectedat the level of individual workers, without iden-tifying the employer, and thus there has notbeen much empirical research about diversity atthe firm level. Further, it is difficult to identifya worker's place in the hierarchy of a firm fromsuch data sources. Our study thus motivates theexploration of alternative data sources. For ex-ample, the data on partnership decisions by in-dividual law firms is publicly available, and itwould be especially appropriate for investigat-ing the importance of mentoring effects.^^ Morebroadly, if firm-level data were available for aset of firms with similar hierarchical structures,it would be interesting to examine how a varietyof individual outcomes (including promotions,hiring, and turnover) depend on the type com-position of the firm at different levels of thehierarchy.

Our model can be extended in a number of

•' Unfortunately, the incidence of female or minoritypartners in law firms was very low during ihe 198O's andearly 1990's, so only more receni data can potentially pro-vide sufficienl variation in diversity of partners.


directions. The extension in our working paperis just a start at developing a full theory ofmentoring and diversity in an economy. Oneeould add endogenous human-capital acquisi-tion by workers, as well as the entry and exit offirms. One could develop a more detailed mi-croeconomic model of mentoring.^^ For exam-ple, one could study the incentives to buildmentoring relationships, or allow the level ofmentoring received by a worker to depend onthe ability of the mentor. More broadly, there isthe possibility to further develop a theory of thefirm based on the accumulation of specializedassets over time [as in Edward Prescott andMichael Visscher (1980)]. The business strat-egy literature highlights a number of assets thatfirms build up over time, such as managementtalent, corporate culture, and organizational ca-pabilities (Ingemar Dierickx and Karel Cool,1994; Jay B. Barney, 1997). One can studyvarious policies based on their effect on theaccumulation of these assets, just as we studypromotion policies based on their effect on thestock of upper-level employees.-''*

APPENDIX

We begin by proving two basic results aboutthe behavior of the dynamic process. Lemma 2demonstrates that the value function is welldefined. Lemma 3 demonstrates the existence ofa steady state for the unbiased and optimalpromotion policies. We then proceed to provethe remaining results, following the order of theresults in the text.

LEMMA 2: The value function defined byequation (1) is unique and continuous. The pol-icy correspondence z* is compact valued andupper semicontinuous. V and \z*{m) - r/2|are both symmetric about m — Vi.

PROOF:In the notation of Nancy Stokey and Robert

Lucas (1989), our one-period payoff function,

^' See Belle Rose Ragins (1997) for a discussion of thispoint.

•* Rafael Rob and Peter Zemsky (1997)—building onthe general approach developed here—explore the effect ofincentive policies on the evolution of a firm's "stock" ofcorporate culture.

F(m, m') = 7r(m, m' - (1 - r)m) is boundedand continuous; the function V{m) = [(1 -r)m, (1 - r)m -I- r], which characterizes thefeasible values of the state variable in the nextperiod, is nonempty, compact valued, and con-tinuous; and the discount rate is in (0, 1). Hencetheir Theorem 4.6 holds for our model and thevalue function is unique and continuous and thepolicy correspondence is upper semicontinuous.The symmetry in V and \z*(m) - r/2\ followfrom the symmetry of our model.

LEMMA 3: (i)M^^(-) is a single-valued,nondecreasing continuous function, andM^^im) > Viform > Vi.

(ii) A/*(-) is upper semicontinuous, and ex-cept for upward jumps, it is a single-valued,nondecreasing, and continuous function. Fur-ther, M*{m) > Viform > Vi.

(iii) With either biased or unbiased promo-tions, the diversity of the firm converges to asteady state in {'/z, 11 for m" > V2 .

PROOF:(i) For M^^i:) nondecreasing, note that

z^^(m) = argmax,g[o^jTT(m, z) and (d^/dmdz)iTim, z) > 0. Since the objective is differ-entiable, strictly concave, and strictly super-modular, z^^(m) must be unique everywhere,and strictly increasing when 0 < z^^(m) < r.(ii) Consider the following expression forM*(m)

M*{m) = argmax Trim, m' - (1 - r)m)

+ 8V{m'),where T{m) = [(1 - r)m, (1 - r)m + r].Note that the preceding objective is strictly su-permodular in m and m' since

(Al)7r(m, m' — (1 — r)m)

dm dm'

= n^'im) -I- /Lt '(l — m)

-x'im' - (1 - r)m)

~ x'(r - m' ~ (I - r)m) > 0.

Further, r(m) is nondecreasing in the strong setorder (see Paul Milgrom and Christina Shan-


non, 1994). Hence, M*(m) is nondecreasingand single valued everywhere except at upwardjumps. Thus, every selection from M*{m) is acontinuous function but for upward jumps, (iii)Clearly, for m > V2 , M^^{m) > V2. Considerm' < V2 and m > Vi. Together, condition(Al) and the symmetry of V implies thatvim, m' - (1 - r)m) + SV(m') < trim. 1 -m' - (1 - r)m) + 8V{\ - m"), whichestablishes that for m > 'A , M*im) > Vi form > V2. By our constraint, M*im) ^ 1 form > V2. Hence, following Milgrom and JohnRoberts (1994), starting from m" > '/z, a fixedpoint of M* and M^^ exists on [V2, 1].

PROOF OF PROPOSITION 1:We proceed by induction on number of peri-

ods remaining in a firm's life. We know thatwhen there is 1 period to go, the value functionis equal to TT^ (m), which is nonincreasing inm ^ V2 when SCV holds everywhere. Considerthe problem with T periods to go, and assumethat the value of the firm with T — 1 periods togo, V^^~ "(m), is nonincreasing in m. The firmthen solves

= max {7r{m, z)

- r)m + z)] .

Observe that (d^/dm dz)'rr(m, z) ^ 0. SinceV*^" "(m) is nonincreasing. clearly z'"(m) ^z'^^(m), and so (a/am)7r(m, z '") < (d/(im)7T{m, z^^) ^ 0. Using this and the enve-lope theorem, {dldm)V^^\m) = {dldm)'n{m,z< ) -H S • (1 - r)V<^- "'((1 - r)m + z'^) < 0.By induction, and since monotonicity is pre-served by infinite sums, the infinite-horizonvalue function is also nonincreasing in m > ' / : .The argument is analogous for SCV holdsnowhere.

PROOF OF PROPOSITION 2:(i) Vi G ^^^ if and only if z'^^'iVz) < r. Using

then M is concave over {Vi, 1], and there is atmost one stable steady state in this interval; thesteady state exists if and only if M'iVi) > 1. Iffi."'(m) < 0 for all m, then M^'^ is convex over ('/2,I], and there are at most two steady states in theinterval, and only state m = 1 can be stable.

PROOF OF PROPOSITION 3:The rankings of ^ * and ^^^ follow by Mil-

grom and Roberts (1994), using our results onthe sign of the bias from Proposition I. Nowconsider the question of whether full diversity isastablesteady state. Recall that z'^^C/z) = r/2.Hence, z*{V2) - z.''^(V2) + biVi) = r/2 ifand only if b(V2) = 0, which is the case whenSCV holds everywhere, but not when SCVholds nowhere. In the case where SCV holdseverywhere, the bias favors the minority, and soif V2 is stable under unbiased promotions, it willalso be stable with optimal promotions.

PROOF OF PROPOSITION 4:For a sufficiently large, z^^ = r and ^^^ -

{0, I} . Further, for a sufficiently large SCVholds nowhere and the bias is for the majority.Hence, by Proposition 3if*- {0, 1} as well.As a ^ 0, z^^ -> r/2 and bim) -^ 0 andhence M*{m) ^ m(l - r) + r/2 so thatcf* ^ {1/2). If ^ is concave, then SCV issatisfied everywhere for a sufficiently small,and from Proposition 2 (ii) the stable steadystate in the neighborhood of V2 is Vz.

PROOF OF PROPOSITION 5:Consider first the parameter y. Recall that

z'''^{m\ r, Q, 7) = argmax.^^o. r]"""('"' ^' ^ "•7), and that {dldz)TT = x(z^'^; y) - jc(r -z^^; y) + a[^l(m) - ^(1 - m}]. By defini-tion, J:(Z^*; y) - x{r ~ z^^\ y) is nonincreas-ing in y for 2 ^ r/2, which holds if m > V2 .Thus, {h'^lbz By)v < 0, and z"^ must benonincreasing in y. But then, z^*/x'(m) - (r—z^^)ix'(a - m) is nonincreasing in y. Considernext the parameter a. Since /x(m) - jLt( 1 —m) > 0 form > Vt, (d^/dz 5a)TT > 0, which

the implicit function theorem, z {V2) = implies that z.UB and - (r --ayJ{V2)lx'{rl2)\ substituting gives the result, (ii)Suppose x{e) = K- yd. Since Af (m) = (1 -r)m + z^^(m), the curvature of M^^ follows thatof z^^. For z"" < 1, z^\m) = 'A r + a{p.{m) -|LL(1 - m))/(2y). Thus, {d^ z'^^I'dm^) = a(fx"(m) -^"(1 - m))/(2y). Hence, if ^L"'{m) > 0 for all m.

- m) are nondecreasing in a. Fi-nally, consider the parameter r and the linearinitial ability function. In this case, (9/dr)z^^ — '/2, and so {d^ldr dm)TT =i/2a[jLt'(m) - /n.'(l - m)]. Thus, if fi isconcave, id/dm)TT^^ is nonincreasing in r.

7S4 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 2000

PROOF OF LEMMA 1:We begin by arguing that the optimal promo-

tion policy is unique at a stable steady state.Recall that Lemma 3 implies that M* is singlevalued almost everywhere, except at upwardjumps. By definition, rm, is one optimal pro-motion policy at state m ,. Suppose that there isanother optimal promotion rule, z' > rm^.Then there must be an upward jump in M* atm/, suppose that the jump is of size d. But thisimplies that for a\\ d > e > 0, M*(m^ + e) >m^ + d > m^ + E, contradicting the definitionof a stable steady state.

Now consider an interior steady state m, ^{0, '/2, 1} and the associated steady statepromotion policy z^ = rm^. Since

dFOCAm; y)

_ d[x{rm; y) ~ x({\ - r)m; y)]dy ~

for m > V2, which holds by definition, (ii)Using

7T|(m,, rm,) = x{rm,) - x{r{l - m j )

m,

, rmj =

- (1 -

= argmax TT{m,, z) + + (1 - r)m,) we have that

it must be that 7r2(m . rmj + 8V'{mJ = 0wherever this derivative exists. To solve for V ,let z = (z ' , z^. •••), and define

dFOCAm; 5)

- m))

I, z) = Tr(m, z')Consider m > 1/2. If u is globally SCV, then

— r)m, z ) + ••• . ^ {m)ix (1 — m) > (r — z (m)}/i'(m).Then z^^(m) > z*(m) = rm implies thatdFOC^{m)ldS > 0. Conversely, if fx is no-

If m,_ is a steady state, then V'{m,) = {dl where SCV, dFOCAm)ldb < 0. (iii) Observew h e r e z_, = (rm^, rm^, •••). By

the envelope theorem, we have that

,, I) = E {1 - _,, rm,)

j , rm,)

first that

d— FOCAtn; a) = - /x(l - m)

rS

- ( 1

Inserting this into the expressionrm^) + SV"(mJ = 0 gives the resuU.

PROOF OF PROPOSITION 6:(i) Applying the implicit function theorem,

since by assumption m, is opfimal, it suffices tocheck that

Suppose that SCV holds nowhere. Observe thatby Proposition 1 and optimality of the stablepromotion policy, SCV nowhere implies thatrm, > z^^{m^). But then, the second term in(dlda)FOCXm\ a) must be greater than {dldm)TT^^{m), which in turn is positive by SCVnowhere. For 6 small, recall that m, G ^^^satisfies z^^im^) - rm, = 0. Consider m, ^V2. Then the diversity of if^^ is increasing

VOL 90 NO. 4 ATHEY ET AL: MENTORING AND DIVERSITY 785

(decreasing) in a parameter if z^^(m,) - rm/isdecreasing (increasing) in that parameter. It isstraightforward to show that 8z^^/^a > 0. (iv)In the linear case, we have

- S)

m; r)fr

= - ( 2 m - l ) y +(1 - { 1 -r)S)'

-m)).

By Proposition 2 and optimality of the stablepromotion policy, SCV everywhere implies thatrm^ < z^^(m,). But then, the second term in{didr)FOCAm; r) must be less than {\lr)idlSm)7r^^(m), which in turn is negative by SCVeverywhere. For S small, we can considerwhether {dldr)iz^^ - rmj < 0, which holdsif dz^'^ldr < m,.

REFERENCES

Arrow, Kenneth. "The Theory of Discrimina-tion," in Oriey C. Ashenfelter and AlbertRees, eds.. Discrimination in labor markets.Princeton, NJ: Princeton University Press,1973, pp. 3-33.

Athey, Susan; Avery, Christopher and Zemsky,Peter. "Mentoring, Discrimination and Diver-sity in Organizations." Stanford GSB Work-ing Paper No. 1317, 1994.

. "Mentoring and Diversity." Mimeo,Massachusetts Institute of Technology, Octo-ber 1998.

Barney, Jay B. Gaining and sustaining compet-itive advantage. New York: Addison-Wesley, 1997.

Bartlett, Robin. "Report of the Committee on theStatus of Women in the Economics Profes-sion." American Economic Review, May 1997{Papers and Proceeding.s), 57(2), pp. 506-10.

Heller, Andrea. "Trends in Occupational Segre-gation by Sex and Race, 1960-1981," in Bar-bara F. Reskin, ed.. Sex segregation in theworkplace. Washington, DC: National Acad-emy, 1984, pp. 11-26.

Bergmann, Barbara. "Does the Market for Wom-en's Labor Need Fixing?" Journal of EconomicPerspectives, Winter 1989, 3{\), pp. 43-60.

Business Week. "White. Male, and Worried."January 31, 1994, pp. 50-55.

Coate, Stephen and Loury, Glenn. "Will Affir-mative-Action Policies Eliminate NegativeStereotypes?" American Economic Review,December 1993, 83{5), pp. 1220-40.

Cornell, Bradford and Welch, Ivo. "Culture, In-formation and Screening Discrimination,"Journal of Political Economy. June 1996,}04{3l pp. 542-72.

Dierickx, Ingemar and Cool, Karel. "Competi-tive Strategy, Asset Accumulation andFirm Performance." in H. Daems and H.Thomas, eds.. Strategic groups and strate-gic moves. Oxford: Pergamon Press. 1994,pp. 63-80.

Dreher, George F. and Cox, Taylor H. "Race.Gender, and Opportunity: A Study of Com-pensation Attainment and the Establishmentof Mentoring Relationships." Journal of Ap-plied Psychology, June 1996. 87(3), pp. 297-308.

Greif, Avner. "Contract Enforceability andEconomic Institutions in Early Trade: TheMaghribi Traders' Coalition." AmericanEconomic Review, June 1993, 83(3), pp.525-48.

"Cultural Beliefs and the Organizationof Society: A Historical and Theoretical Re-flection on Collectivist and Individualist So-cieties." Journal of Political Economy,October 1994. 702(5). pp. 912-50.

Iharra, Herminia. "Homophily and DifferentialReturns: Sex Differences in Network Struc-ture and Access in an Advertising Firm."Administrative Science Quarterly, September1992, i7(3), pp. 422-47.

Jones, Del. "Setting Diversity's Foundation inthe Bottom Line." USA Today. October 15.1996. p. 4B.

Kanler, Rosabeth. Men and women of the cor-poration. New York: Basic Books. 1977.

Milgrom, Paul and Roberts, John. "ComparingEquilibria." American Economic Review,June 1994, 84{3), pp. 441-59.

Milgrom, Paul and Shannon, Christina. "Mono-tone Comparative Statics," Econometrica,January 1994. 62(1), pp. 157-80.

Morrison, Ann and Von Glinow, Mary Ann."Women and Minorities in Management."American Psychologist, February 1990,45(2), pp. 200-08.


National Law Journal. "Women' s ProgressSlows at Top Firms." May 6, 1996, p. Al.

Noe, Raymond. "Women and Mentoring: A Re-view and Research Agenda." Academy of Man-agement Review. Swoj^ay 1988, /i(l), pp. 65-78.

Prakash, Gautam. The insider's guide to man-agement consulting. San Francisco: Wet FeetPress, 1995.

Prescott, Edward and Visscher, Michael. "Orga-nization Capital." Journal of Political Econ-omy, June 1980, 88(3), pp. 446-61.

Ragins, Belle Rose. "Diversified Mentoring Re-lationships in Organizations: A Power Per-spective." Academy of Management Review,April 1997, 22(2), pp. 482-521.

Rob, Rafael and Zemsky, Peter. "Cooperation,Corporate Culture and Incentive Intensity."INSEAD Working Paper Series, 1997.

Rosen, Asa. "An Equilibrium Search-MatchingModel of Discrimination." European EconomicReview, August 1997, 4/(8), pp. 1589-613.

Rothstein, Donna. "Supervisor Gender, Race,and Ethnicity and the Labor Market Out-comes of Young Workers." Mimeo, U.S. Bu-reau of Labor Statistics, Washington, DC,1997.

Spurr, Stephen. "Sex Discrimination in the Le-gal Profession: A Study of Promotion." In-dustrial and Labor Relations Review, April1990, 43(4), pp. 406-17.

Stokey, Nancy and Lucas, Robert. Recursivemethods in economic dynamics. Cambridge,MA: Harvard University Press, 1989.

Wall Street Journal, The. "Workplace: Labor'sMartin is Out to Break the Glass Ceiling."August 9, 1991, p. Bl.

"Women Make Strides, But Men StayFirmly in Top Company Jobs." March 29,1994, p. Al.

Wallman, Steven. "Equity Is More Than 'Ordi-nary Business" " New York Times, March 30.1997, p. 3.

mentoring and diversity - harvard university and...mentoring and diversity bv susan athey,...

Documents