Why Do I Like People Like Me?

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1 Wy Do I Like People Like Me? Manuel Bagues Maria J. Perez-Villaoniga Fortcoming in Journal of Economic Teory Abstract In tis paper we exten te stanar moel of statistical iscrimination to a multiimensional framework were te accuracy of evaluators epens on ow knowlegeable tey are in eac imension. Te moel yiels two main implications. First, caniates wo excel in te same imensions as te evaluator ten to be preferre. Secon, if two equally prouctive groups of workers iffer in teir istribution of ability across imensions group iscrimination will arise unless (i) evaluators are well informe about te extent of tese ifferences an (ii) evaluators can take caniates group belonging into account in teir assessments. JEL coes: J71, D82 Keywors: Statistical iscrimination, similar-to-me effect. We woul like to tank Antonio Cabrales, Juan Jose Dolao, Florentino Felgueroso, Walter García-Fontes, Juan F. Jimeno, Günter Fink, Marco Haas, Franck Malerbet, Pero Marín, Euaro Melero, Nicola Pavoni an Enrico Pennings for many useful comments on an earlier version of tis paper. We are also grateful to participants in seminars at te universities of Bocconi, Verona, Pavia, Las Palmas e Gran Canaria, Ovieo, León, Sant Anna Scool of Avance Stuies, FEDEA an conference presentations at te JEI, SAE an SOLE-EALE. We acknowlege te financial support of te Social Sciences an Humanities Researc Council of Canaa an te Spanis Ministry of Science an Tecnology (researc grants ECO C05-05, ECO an ECO ). All remaining errors are our own. Corresponing autor. mfbagues@emp.uc3m.es. Universia Carlos III e Mari, C/ Mari 126, Getafe, Spain. Pone: Fax: Universia e Ovieo. mjpvilla@uniovi.es 1

2 1 Introuction Te fact tat iniviuals migt be treate ifferently accoring to exogenous caracteristics suc as gener, age or race as been well ocumente in te literature. Most of te evience refers to te labor market, were ifferences in wages or iring an promotion tat cannot be accounte for by ifferences in prouctivity ave been observe. 1 In te economics literature, two istinct general sets of explanations ave been propose to explain te origin an persistence of iscrimination. On te one an, taste moels, as in Gary Becker s [5] seminal work, suggest a preference-base motivation for te existence of iscrimination. Te ifference in wages between two equally prouctive groups of workers arises because employers, customers or co-workers islike interacting wit employees tat belong to certain groups. On te oter an, statistical moels of iscrimination argue tat, in te presence of information asymmetries about te real prouctivity of workers, te group-belonging of an iniviual can be consiere as a signal tat provies aitional information. In tis context, taking into account an iniviual s group affiliation may be a rational response to its informational content. Groups of workers may iffer in teir expecte prouctivity (Pelps [20], Lazear an Rosen [18]) or in te reliability of te observable signals (Aigner an Cain [1], Cornell an Welc [10]). Arrow [3] proposes an alternative moel were employers asymmetric beliefs about te uman capital investments of members of ifferent groups are self-confirming an iscriminatory outcomes can be tougt of as te result of a self-fulfilling propecy. Coate an Loury [9] furter formalize tis approac. 2 1 For a survey see, for instance, Altonji an Blank [2]. Discriminatory beaviors ave also been observe in ousing ecisions (Massey an Denton [19], lening (Hunter an Walker [16]), car selling (Ayres an Siegelman [4]) or even in te refereeing of acaemic papers (Blank [6], Fiser et al. [13]). 2 For a recent review of teoretical moels of statistical iscrimination see Fang an Moro [12]. 2

3 In tis paper we exten te stanar moel of statistical iscrimination presente by Pelps [20] introucing two novel features. First, we allow for te existence of multiple imensions of ability. Tese imensions can be unerstoo eiter as ifferent tasks tat te worker nees to unertake, or as separable skills tat are require to perform a single task. Secon, we assume tat te capability of an employer to evaluate quality at a certain imension increases wit er knowlege of tat imension. 3 Tis assumption is consistent wit experimental evience, were it as often been foun tat, in many imensions, iniviuals wo are less competent are also relatively less accurate at evaluating ability. 4 Combining tese features te moel yiels te following two preictions. First, we sow tat a similar-to-me-in-skills effect arises in te evaluation. Since iniviuals can assess knowlege more accurately at tose imensions were tey are more knowlegeable, an employer wo makes an optimal use of te available information will give relatively more weigt to signals observe in imensions were se is most knowlegeable. As a result, given any two equally prouctive caniates, te employer will ten to give a iger valuation to te caniate wo excels in te same imensions as se oes. Secon, te moel sows tat, even if members of ifferent groups are equally prouctive, group iscrimination migt arise if groups iffer in teir istribution of ability across imensions. 5 In particular, group iscrim- 3 It may be possible to rationalize tis assumption witin a categorical moel of cognition (Fryer an Jackson [14]). Accoring to tis moel, evaluators process information wit te ai of categories. If te number of categories is limite, tose types of experiences tat te evaluator faces less frequently are more coarsely categorize. As a result, evaluators woul make less accurate preictions wen confronte wit suc experiences. We tank an anonymous referee for making tis point 4 Knowlegeable people are more accurate in teir evaluations in te fiel of cess (Ci [7]), pysics (Ci et al. [8]), grammar (Kruger an Dunning [17]) or acaemic performance (Everson an Tobias [11]). 5 Following Aigner an Cain [1], we consier group iscrimination as te situation were groups tat ave te same average ability may receive ifferent average pay (pp. 178). Note tat in a multiimensional framework te term same ability soul be interprete as meaning same total ability rater tan same ability at every imension. 3

4 ination will arise if (i) employers are not fully aware of te extent of tese ifferences or (ii) employers are perfectly informe but cannot conition teir evaluations on caniates group-belonging. Te intuition bein tis result is te following. Employers will ten to give more weigt to signals tat ave been observe in tose imensions were tey are more knowlegeable. In principle tis favors caniates belonging to te same group as te employer, as tey are more likely to excel precisely in tese imensions. Still, a well-informe evaluator wo was allowe to take into account te group belonging of caniates migt ajust er priors appropriately. Tis woul not only be efficient from an informational point of view but, as well, it woul yiel similar average evaluations across groups of caniates. Te moel propose in tis paper iffers in several ways from Pelps [20] an from oter relate moels of statistical iscrimination (Aigner an Cain [1], Cornell an Welc [10]). Tese moels rely on te existence of some exogenous group ifference in te quality of signals. Here te source of iscrimination is an exogenous group ifference in te istribution of quality across imensions, but all groups are being evaluate wit te same accuracy. Tere are also substantial ifferences in terms of te preictions of te moel in at least two respects. First, stanar moels preict tat among igly prouctive caniates, tose belonging to te evaluator s group will ten to be ire but, wen all caniates are relatively unprouctive, tose wo o not belong to te employer s group will ten to be preferre, given tat te observe (low) signal is a weaker inicator of teir prouctivity. Still, up to our knowlege tere is no empirical evience supporting te latter implication, tis is, te reversal of te race an gener gap for low prouctivity levels. In contrast, in te (multiimensional) moel propose ere tose caniates akin to te evaluator ten to be preferre for every level of prouctivity. Secon, in stanar moels, iing te ientity of can- 4

5 iates eliminates iscrimination. In tis framework te opposite is true: evaluators will ten to prefer caniates from teir own group unless tey take into account caniates group belonging. In sum, wen te accuracy of evaluators at eac imension epens on ow knowlegeable tey are, blin evaluations may generate iscriminatory outcomes. 2 Te moel Let us consier te case of an iniviual i wose total quality q i epens on is abilities or skills in a number D of ifferent imensions or fiels. Tese fiels can be unerstoo as ifferent tasks tat te worker nees to unertake or as separable skills tat are require to perform a single task. For simplicity, we will assume tat caniate s total prouctivity is equal to te sum of is [ quality at eac imension q i = x i ]. D Caniates abilities are assume to be exogenously given an inepenently an normally istribute. Witout loss of generality, we impose two simplifying assumptions on te population istribution of quality. First, we restrict te variance of quality to be equal across imensions an normalize it equal to one. Wit tis constraint we want to avoi a more general case were ability may vary systematically more along certain imensions. Secon, we assume tat an iniviual s ability along a certain fiel is inepenent of is ability along any oter imension. In oter wors, te knowlege of an iniviual s ability in one imension oes not provie any information about is ability in any oter imension. 6 Tis is, x i N (p, I), were p is a Dx1 vector of mean abilities an I is an ientity matrix. In tis multiimensional framework let us consier te case were ini- 6 As long as tere exists some kin of multiimensionality, tis is, provie tat quality in ifferent imensions is not perfectly correlate, imensions coul always be appropriately reefine suc tat tis conition is satisfie. 5

6 viuals total prouctivity is not observable but an evaluator can observe some imperfect signal of caniates ability at eac imension. Tese signals coul be interprete as te result of some tests or job interviews an teir value will be a function of te caniates true ability at eac fiel plus an error term η wic is assume to be inepenently an normally istribute wit zero mean an finite variance. y i = x i + η i ) were ηi N (0, σ η Moreover, let us assume tat in eac imension te accuracy of te signal is inepenent of te quality of te caniate: E ( x i ηi) = 0 Given te above assumptions, te evaluator will infer te quality of caniate i in imension as te weigte sum of te signal observe in tis imension an te istributional prior, were te weigt given to te signal will epen on ow accurately tis signal is perceive by te evaluator: E (x i /y i ) = γ y i + ( 1 γ ) p (1) were γ = E (x i y i ) E (y i y i ) = 1 1+σ η an te conitional expecte total prouctivity is equal to: E (q i /y i1,..., y id ) = D [ γ y i + ( 1 γ ) p ] Tis is, employer will take relatively more into account tose signals tat se observes in fiels were se can assess information more accurately. 2.1 Similar-to-me-in-skills effect Let us efine an evaluation as being complex if an evaluator s relative ability to assess quality is positively relate to er own quality. In a context were, 6

7 witout loss of generality, D is equal to two, an evaluation is complex if, given an evaluator : x 1 > x 2 = σ η 1 < σ η 2 It easily follows tat wen te evaluation is complex, an evaluator wo makes an optimal use of te available information will give a larger weigt to tose signals tat ave been observe in tat imension were er own ability is larger. Tis is, x 1 > x 2 = γ 1 > γ 2 (2) As a result, face wit two equally prouctive caniates i an j, evaluator will ten to give a iger evaluation to te caniate wo excels in te same imension were se erself is best. More precisely, Proposition 1 Similar-to-me-in-skills effect q i = q j, x 1 > x 2 & x i1 > x j1 E [q i ] > E [q j ] Proof. Te ifference in te expecte quality of te two caniates is equal to: [ ( E [q i ] E [q j ] = E γ y i + ( ) ) ] [ ( 1 γ p E γ y j + ( ) ) ] 1 γ p = =1,2 =1,2 = ( γ x i + ( ) ) ( 1 γ p γ x j + ( ) ) 1 γ p = γ (x i x j ) =1,2 =1,2 =1,2 wic is positive since x i1 x j1 = x j2 x i2 > 0 an, by (2), γ 1 > γ 2. 7

8 2.2 In-group bias We investigate weter te existence of te above similar-to-me-in-skills effect can generate an in-group bias. Let us consier tat iniviuals may belong to two ifferent groups g 1 an g 2 efine accoring to gener, age, or some oter easily observable an exogenous caracteristic. Let us assume tat caniates total prouctivity is inepenent of group belonging: E [q i /i g 1 ] = E [q j /j g 2 ] (3) Tis assumption oes not prevent te possibility tat members of te two groups ten to excel in ifferent imensions. More particularly, let us represent te existence of group-relate variations in te istribution of quality in te following way: x i = p (g) + µ i = 1, 2; i g were p (g) is te expecte ability in imension of iniviuals in group g an µ is assume to be normally an inepenently istribute wit zero mean an variance equal to one. For simplicity, we consier te case were te istribution of quality across groups is symmetric an group g 1 as a iger mean in imension one. p (g 1) 1 = p (g 2) 2 = p 1 > p 2 = p (g 1) 2 = p (g 2) 1 (4) In our analysis we consier two possible scenarios. First, evaluators observe bot caniates signals of quality an also teir group belonging. Secon, we stuy te case were employers may take into account caniates observable signals of quality but cannot observe caniates group belonging. 8

9 2.2.1 Non-blin evaluations If employers observe tat employees belonging to certain groups ten to perform better on certain imensions, employers will take into account tis information in teir evaluations. In tis set up, evaluators estimate caniates quality in a similar way as in (1). Given tat y i = x i + ηi, it follows tat in eac imension te relationsip between quality an signal, net of ( ) te group effect, will be equal to x i p (g) = γ y i p (g) + u i. Tus, E (x i ) = E [γ y i + ( ) ] 1 γ (g) p were γ = V ar(µ i ) V ar(µ i )+V ar(ηi) = 1. 1+σ η If te evaluator can conition er evaluation on te observe signals an on te group belonging of caniates, ten any two equally prouctive caniates ten to obtain te same valuations inepenently of group belonging. Proposition 2 Non-blin evaluations yiel non-iscriminatory outcomes E [p i / i g 1 ] = p (g 1) ; E [p j / j g 2 ] = p (g 2) = E (q i /i g 1 ) = E (q j /j g 2 ) = 1, 2 Proof. E (q i /i g 1 ) E (q j /j g 2 ) = [ ( E γ y i + ( [ ) ) ( 1 γ pi /i g1 ] E γ y j + ( ] ) ) 1 γ pj /j g2 = =1,2 = =1,2 ( γ p (g 1) + ( 1 γ =1,2 ) (g p 1 ) ) ( γ p (g 2) + ( 1 γ =1,2 ) ) (g p 2 ) = {by (3)} = 0 In summary, if well-informe employers may conition teir evaluation on te group belonging of caniates, te outcome of evaluations will be inepenent of employers group belonging. 9

10 2.2.2 Blin evaluations Let us consier te case wen evaluators cannot observe caniates group belonging. Witout loss of generality, we will assume tat it is common knowlege tat tere are two groups of equal size [P (i g 1 ) = P (i g 2 )]. Evaluators will infer caniates group belonging base on te observe signals. In particular, if te evaluator observes signals y i1 an y i2, er best guess about caniate i s group belonging to group l is given by: P (i g l /y i1, y i2 ) = P (y i1, y i2 /i g l ) P (i g l ) P (y i1, y i2 /i g k ) P (i g k ) = P (y i1, y i2 /i g l ) P (y i1, y i2 /i g k ) k=1,2 k=1,2 Base on te observe signals an te inferre group belonging, evaluator will estimate te quality of caniate i as follows: E (q i / y i1, y i2 ) = [ ( = E γ y i + ( ] ) ) 1 γ pi /yi1, y i2 = ( γ y i + ( ) 1 γ E (p i /y i1, y i2 ) ) =1,2 =1,2 were E (p i / y i1, y i2 ) = P (i g 1 /y i1, y i2 ) ( ) p (g 1) p (g 2) + p (g 2) If signals are not fully informative about caniates group belonging, caniates tat belong to te evaluator s group ten to be favore. 7 Proposition 3 Blin evaluations yiel iscriminatory outcomes P (i g 2 /i / g 2 ) > 0; P (j g 1 /j / g 1 ) > 0 = E (q i /i, g 1 ) > E (q j /j g 2, g 1 ) were P (k g l /k / g l ) represents te likelioo tat caniate k is assigne to te wrong group by evaluator. 7 Te extreme case were signals provie perfect information about caniates group belonging correspons to a setup were iniviuals from ifferent groups cannot eliver similar signals. In suc context, evaluations woul be in practice non blin. 10

11 Proof. Witout loss of generality let us consier te case were te evaluator is a typical group g 1 member suc tat x 1 > x 2. E (q i /i g 1 ) E (q j /j g 2 ) = = [ γ p (g 1) + ( ) 1 γ E (p i /i g 1 ) ] =1,2 = =1,2 =1,2 =1,2 [ γ p (g 1) + ( 1 γ ) [P (i g 1 /i g 1 )] [ γ p (g 2) + ( 1 γ ) [P (j g 1 /j g 2 )] [ γ p (g 2) + ( ) ] 1 γ E (p j /j g 2 ) = ( ) p (g 1) p (g 2) ( ) p (g 1) p (g 2) ] + p (g 2) = [ (γ 1 γ 2 ) (p 1 p 2 ) ] [P (i g 2 /i g 1 ) + P (j g 1 /j g 2 )] ] + p (g 2) = {by (4)} = wic is positive since γ 1 > γ 2, p 1 > p 2 an P (k g l /k / g l ) > 0, k = i, j 3 Conclusion In tis paper we buil on te stanar moel of statistical iscrimination were an employer must select a caniate in a context of imperfect information. Our main eparture from te traitional framework is to allow for te existence of multiple imensions of ability an to make te accuracy of te evaluation at eac imension epen on te evaluators knowlege of tis imension. Te moel yiels two main results. First, it rationalizes te existence of a similar-to-me-in-skills effect wic favors caniates wo excel in te same imensions as te evaluator. Secon, te moel casts oubts on te capability of blin evaluations to eraicate iscrimination. If groups of iniviuals iffer in teir istribution of ability across imension, an ingroup bias may arise unless evaluators are well informe about te extent of tese ifferences an, moreover, tey can observe caniates group be- 11

12 longing. Several reasons may prevent evaluators from taking into account te group belonging of caniates. Evaluators may not be aware of te existence of ifferences in quality profiles across groups. Tis may appen wen groups ave little interaction, peraps because te size of te minority is relatively small, 8 or in te presence of a number of cognitive biases suc as observational selection bias, availability bias or ancoring tat can generate a ivergence between iniviuals perception of oter groups quality at eac imension an teir true quality istribution. As well, even if evaluators are well informe about tese ifferences, tey may be restricte not to use tis information. Tis is te case, for instance, in many firms an institutions were caniates ientity is kept anonymous (as in Blank [6] or Golin an Rouse [15]). Paraoxically, in te framework consiere ere, tese policies may aggravate iscrimination. References [1] Aigner, D. J. an G. Cain (1977), Statistical Teories of Discrimination in Labor Markets, Inustrial an Labor Relations Review, 30(2) pp [2] Altonji, J.G. an R. M. Blank (1999), Race an Gener in te Labor Market in O. Asenfelter an D.Car. (Es.), Hanbook of Labor Economics, vol. 3, Nort-Hollan, Amsteram, pp [3] Arrow, K. J. (1973), Te Teory of Discrimination in O. Asenfelter an Albert Rees (Es.), Discrimination in Labor Markets, Princeton University Press, Princeton, NJ, pp As it woul increase te cost of rationality. See for instance Fryer an Jackson [14]. 12

13 [4] Ayres, I. an P. Siegelman (1995), Race an Gener Discrimination in Bargaining for a New Car, American Economic Review, 85(3), pp [5] Becker, G. S. (1957), Te Economics of Discrimination, University of Cicago Press, Cicago. [6] Blank, R. M. (1991), Te Effects of Double-Blin versus Single-Blin Reviewing: Experimental Evience from Te American Economic Review, American Economic Review, 81(5), pp [7] Ci, M. T. H. (1978), Knowlege structures an memory evelopment in R. Siegler (E.), Cilren s tinking: Wat evelops?, Erlbaum, Hillsale, NJ, pp [8] Ci, M. T. H., Glaser, R. an E. Rees (1982), Expertise in problem solving in R. Sternberg (E.), Avances in te psycology of uman intelligence, Erlbaum, Hillsale, NJ, Vol. 1, pp [9] Coate, S. an G. C. Loury (1993), Will Affirmative-Action Policies Eliminate Negative Stereotypes?, American Economic Review, 83(5), pp [10] Cornell, B. an I. Welc (1996), Culture, Information, an Screening Discrimination, Journal of Political Economy, 104(3), pp [11] Everson, H. T. an S. Tobias (1998), Te Ability to Estimate Knowlege an Performance in College: A Metacognitive Analysis, Instructional Science, 26, pp [12] Fang, H. an A. Moro (2010), Teories of Statistical Discrimination an Afirmative Action: a Survey in J. Benabib, A. Bisin, an M. 13

14 Jackson (Es.), Hanbook of Social Economics, Vol. 1, Nort-Hollan, Amsteram, pp [13] Fiser, M., Stanfor B., Frieman M.D. an B. Strauss (1994), Te Effects of Blining on Acceptance of Researc Papers by Peer Review, Journal of American Meical Association, Vol. 272(2), pp [14] Fryer, R. G. an M. O. Jackson (2008), A Categorical Moel of Cognition an Biase Decision Making, Te B.E. Journal of Teoretical Economics (Contributions), 8(1), article 6. [15] Golin, C. an C. Rouse (2000), Orcestrating Impartiality: Te Impact of Blin Auitions on Female Musicians, American Economic Review, 90(4), pp [16] Hunter, W. C. an M. B. Walker (1996), Te Cultural Affinity Hypotesis an Mortgage Lening Decisions, Journal of Real Estate, Finance an Economics, 13(1), pp [17] Kruger, J. an D. Dunning (1999), Unskille an Unaware if It: How Difficulties in Recognizing One s Own Incompetence Lea to Inflate Self-Assessments, Journal of Personality an Social Psycology, 77(6), pp [18] Lazear, E. P. an S. Rosen (1990), Male-Female Wage Differentials in Job Laers, Journal of Labor Economics, 8(1), pp [19] Massey, D., an N. Denton (1993), American Apartei: Segregation an te Making of te Unerclass, Harvar University Press, Cambrige, Mass. [20] Pelps, E. (1972), Te Statistical Teory of Racism an Sexism, American Economic Review, 62(4), pp