DISCUSSION PAPER SERIES IZA DP No. 2764 Implicit Discrimination in Hiring: Real World Evidence Dan-Olof Rooth April 2007 Forschungsinstitut zur Zukunft der Arbeit Institute for the Study of Labor Implicit Discrimination in Hiring: Real World Evidence Dan-Olof Rooth Kalmar University, CReAM and IZA Discussion Paper No. 2764 April 2007 IZA P.O. Box 7240 53072 Bonn Germany Phone: +49-228-3894-0 Fax: +49-228-3894-180 E-mail: [email protected] Any opinions expressed here are those of the author(s) and not those of the institute. Research disseminated by IZA may include views on policy, but the institute itself takes no institutional policy positions. The Institute for the Study of Labor (IZA) in Bonn is a local and virtual international research center and a place of communication between science, politics and business. IZA is an independent nonprofit company supported by Deutsche Post World Net. The center is associated with the University of Bonn and offers a stimulating research environment through its research networks, research support, and visitors and doctoral programs. IZA engages in (i) original and internationally competitive research in all fields of labor economics, (ii) development of policy concepts, and (iii) dissemination of research results and concepts to the interested public. IZA Discussion Papers often represent preliminary work and are circulated to encourage discussion. Citation of such a paper should account for its provisional character. A revised version may be available directly from the author. IZA Discussion Paper No. 2764 April 2007 ABSTRACT Implicit Discrimination in Hiring: Real World Evidence* This is the first study providing evidence of a new form of discrimination, implicit discrimination, acting in real economic life. In a two-stage field experiment we first measure the difference in callbacks for interview for applicants with Arab/Muslim sounding names compared to applicants with Swedish sounding names using the correspondence testing methodology. In the second stage of the experiment we measure, for a sample of the recruiters involved, their explicit and implicit attitudes/performance stereotypes by the means of explicit questions and the implicit association test (IAT). We find (i) only weak correlations between explicit attitudes/performance stereotypes and implicit performance stereotypes but (ii) a strong and statistically significant negative correlation between the implicit performance stereotypes and the callback rate for an interview for applicants with Arab/Muslim sounding names, but not for applicants with Swedish sounding names. These results indicate that implicit discrimination acts differently compared to explicit discrimination and that it is an important determinant of the hiring process. JEL Classification: Keywords: J64, J71 implicit attitudes and stereotypes, discrimination, situation testing, exit from unemployment Corresponding author: Dan-Olof Rooth Kalmar University College 391 82 Kalmar Sweden E-mail: [email protected] * I thank Jens Agerström, Per Johansson, Olof Åslund, participants at seminars in Kalmar and at IFAU (Uppsala) fpr valuable comments and helpful suggestions. Magnus Carlsson, Rickard Carlsson, Klara Johansson, and Terese Johansson provided excellent research assistance. A research grant from the Swedish Council for Working Life and Social Research and another research grant from the Institute for Labour Market Policy Evaluation (IFAU) are gratefully acknowledged. * + 3) / * 38 * + 3 / 1 2 * 3 ; < 1 = + 3 >??(23 * + + @ A @ A 3> B @= A ; * * * + 1 ; 4 C >??D23 4 3 * 1 3 / 2 $ * 1>??D2 3 + 3 E F ) 5 > 5 < C " E C 1)GG'2 + + 3 1>??)2 + 1)GGG23 1 < E ! 3 1>??(2 1 E >??>23 4 + E B 5 " H <# 3 + 3 ! 1>??(2 ) DD> E 5 + 3 4 1 "42 )GG? ; I 1)GGJ23K " , 1>??(2 * . "4 5 " <# 3 4 1>??D2 " 1 2 <# 3 * 3' " )GK 3 " "4 " <# 5 + 3= 3 4 3 5 + K " * ; < "4 * 3 6 ; ' > * + 3 E 3 E 3 2 35 K < ' 3 5 D + 1 "4 3 " 2 * * + + H * 3 4 3 2. A model of implicit and explicit discrimination in hiring 3 5 " <# L 3 3 " <# 5 C 1>??D2 3 + < + 3 * 3 Assume that the probability to receive a callback for a job interview and ethnic discrimination have the following relationship for individual i belonging to ethnic group j: (1) - 1 = 12 = β + δ ; j=Arab/Muslim or native Swede. where X is a vector of characteristics in the job application, which by construction of the experiment is the same for both ethnic groups, is the return to those characteristics for 3 ethnic group j, while is a measure of the degree of ethnic discrimination against group j, expected to be zero against native Swedes. In economics several forms of ethnic discrimination have been modelled (see the survey by Altonji and Blank, 1999). For our purposes we focus on two of those, preference based discrimination and statistical discrimination, both of which can be regarded as explicit forms of discrimination.5 As mentioned in the introduction the aim of this study is to test whether also implicit forms of discrimination are important in the hiring situation. Hence, we can rewrite Equation 1 as: (2) = 12 - 1 = β +δ +δ +δ where the three discrimination terms express explicit preference discrimination, explicit statistical discrimination and implicit discrimination, respectively. One might wonder if it is possible to divide also the implicit discrimination measure into preferences/attitudes and stereotypes as is done for the explicit discrimination measure. 6 Agerström et al (2007) implicit attitude score and the implicit stereotype score have a correlation of above 0.5 indicating that they measure, if not exactly the same, but then at least highly related constructs.& H 3 4 * " # D >??D / >??& E / 35 + 1)GGJ2 3 & 4 "4 3 "4 "4 * @ "4 A @ H A3 + + 3 4 5 + + 3 4 I + < + 3 4 1 < 2 + + 3 4 + " 1 7 # >??? 5 8+ >??K23 5 * / " 3 5 <# 34 H 5 " <# 5 3 4 "43 4 * pplicants had identical human capital within occupations and 34 were on average 25-30 years old, had two to four years of work experience in the same occupation as the job applied for and had obtained their education in the same type of school, but at different locations. Through the schooling information it is signalled that the Arab/Muslim applicant is born in Sweden, but has a non-native Swedish name. Further, the application consisted of a quite general biography on the first page and a detailed CV of education and work experience on the second page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eeling thermometer they were asked to rate their positive or negative feelings on a ten-point scale (1 = very negative feelings, 10 = very positive feelings) toward Arab-Muslim minority men and native Swedish men, and then a difference between the two scales was calculated. This question is identical to the one used by Greenwald et al. (1998) and Nosek et al. (2005). Second, in the Hiring preference rating participants had to choose which group they prefer when hiring people. Rather than being directly related to the IAT, hiring preferences are supposed to measure actual discrimination. The employers/recruiters had to choose one of the following five alternatives: “When hiring staff, I strongly prefer Arab-Muslim men (in Sweden) to native Swedish men”, “When hiring staff, I moderately prefer Arab-Muslim men (in Sweden) to native Swedish men”, “When hiring staff, I prefer Arab-Muslim men (in Sweden) and native Swedish men equally much”, “When hiring staff, I moderately prefer native Swedish men to Arab-Muslim men (in Sweden)”, and “When hiring staff, I strongly prefer native Swedish men to Arab-Muslim men (in Sweden)”. The participants’ responses were coded from -2 to +2, with 0 as an intermediate point reflecting no preference when hiring staff. Third, in the Performance stereotype rating participants choose which of the two groups in question they consider to be more productive at work. The response alternatives were “Arab-Muslim men (in Sweden) are much more productive at work than native Swedish men”,” Arab-Muslim men (in Sweden) are slightly more productive at work than native Swedish men”, “Arab-Muslim men (in Sweden) and Swedish men are equally productive at work”, “Swedish men are slightly more productive at work than ArabMuslim men”, “native Swedish men are much more productive at work than ArabMuslim men”. Again, the participants’ responses were coded from -2 to +2, with 0 as an 8 intermediate point reflecting neutrality. 4 H ) 5 @ A 3 * 1D'O2 1'DO2 E E 5 1(( 4 H " * <# 2 >3 " * 3 5 " <# H 3 4 ' " > !" 4 " 4 1 "42 3 s a computer based test designed to specifically measure individual differences in relative associations between two concepts. It was first introduced by Greenwald et al. (1998) and has since become a widely used measure, particularly in sensitive areas such as attitudes and stereotypes toward social groups.9 The test is illustrated by the Arab-Muslim performance stereotype IAT found in " , . In this computer 3 1>??(2 based version participants first classify, as fast as possible, Swedish and Arab/Muslim sounding names appearing in the middle of the screen according to the (target) category to which they belong, “Arab-Muslim men” or “Swedish men”. In the next part of the IAT the participant now instead classifies words that are found being associated with high and low work productivity. These include words such as “lazy”, “slow”, “efficient” and “hard-working”. In the third step names and high/low work productivity words appear at G 5 9<< 3 3 "43 9 random. The intuitive idea is that it will be easier, and hence, go faster, to classify names and words that are compatible than those that are incompatible. The IAT measures every latency in response to the presented stimulus. For example, when two categories are “easily” associated in terms of their nominal features (Arab names + low work productivity and Swedish names + high work productivity) the participant classifies the stimuli much faster and with fewer errors than when they are not associated. A total of sixty stimuli are presented for the compatible and compatible part, respectively. The difference in response latencies, or rather a recalculation of this difference called Greenwald’s D (as opposed to Cohen’s d), between the compatible and incompatible parts is known as the IAT effect or the IAT score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on-linear effects of the implicit discrimination measure have so far been neglected. When introducing a cubic of the standardized IAT score into the regression model C, for the full as well as the conditional sample, we find that the correlation is much stronger for values of the IAT effect above 0.6, i.e. for strong negative attitudes, see Figure 2 and 3. A related issue is whether there exists a significant interaction effect between the implicit and explicit discrimination measures. However, such an interaction effect is not easily )& " * + 3 13 interpreted with the “continuous” explicit and implicit discrimination measures. Therefore we have constructed binary explicit and implicit “equivalents”. 4 4 '" < * 4 'C3 4 "4 34 ?3' * F < 5 " <# " F 34 <# < 3 " " # <# &( E 34 4 * '" 3 6 * # / 4 '!3 4 3 4 < * < * + * < < 3 4 * 1 # 23 / * * " <# 3 4 + < * )) 14 * " <# 34 6 H 4 3 ' + 5 < * # 3 / 8 3 " * + 34 F * 3 4 * * 3 / + )( * 1 4 - 23 '" 'C '! . ' & F 1 2 < 1 2 3 4 * )GK " 5 + KJ& 36 < * 3" 4 )3 4 * < ; 34 4 D 1# * "2 " )( 4 * * " # 3 15 5 1# C 3" !2 + * 36 1# 2 + 3 * * H + 3 * 3 4 >(& * 3 4 / D # Since the explicit discrimination measures are collected by interviewing recruiters it is likely that some are reluctant to reveal their true attitudes, for instance, for political correctness reasons. Such measurement errors will bias the estimates of the explicit discrimination measures. Also, the empirical analysis reveals that the estimates for the explicit measures are unstable across specifications, indicating measurement problems. A well known strategy is then to find an instrumental variable and estimate IV 2SLS, which helps in deleting the measurement error. This is achieved by having a second measure of explicit preferences that is not perfectly correlated with the first one. Such an instrumental variable exists for the explicit attitude as well as for the explicit stereotype measure. In the case of the explicit attitude measures there are two questions being asked. Hence, the feeling thermometer will be used as an instrument for the hiring preference. For the explicit stereotype measure the IAT measure will be used as an instrument. 6 Q >575 * 4 &3 I 3 * 4 ' D * 3 16 ( 4 + * * 36 "4 " < <# 34 E # " <# F 5 3 " * * E " <# 3 4 * E " + 3 <# . 1>??D2 " <# 3 6 * E 3 E @ A + N 34 " * * + "4 3 / * 3 * * 35 + 3 E 35 "4 3 8 + 3 # 17 strategy as ours are needed before fully accepting implicit discrimination as a new form of labor market discrimination. 18 ) " , %3 ! 6 +- " " E %3 " K)'KBK>DG3 . C 3 + 1 ! 3 1>??(2 @8 5 5 3 1)GGG2 2 B8 A 3 I 7 38 # + 3 3" 3 3 1>??D2 ”Shifts in Attitudes and Labor Market Discrimination: 3 Swedish Experiences after 9-11”, Journal of Population Economics 18 (4), pp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osek, B. (2005) ”Moderators of the relationship between implicit and explicit evaluation”, Journal of Experimental Psychology, vol 134, pp. 565-584. Nosek, B., Greenwald, A. and Banaji, M. (2007) ”The Implicit Association test at Age 7: A Methodological and Conceptual Review”, %3 C 18 32 " $ -3 "3 A * %3 1>??>2 @/ ))> 3 $ " - 3 >&D >G>3 - %3 # G?1K2 8+ - 3 * 3 /'J? /D)J3 + %3 1>??K2 T0 5 3 8 + )& 1'2 3 (J(BJ)'3 -3 1>??D2 @8 ! 3 DDK D&>3 T C A 94 % " 20 0 / )3 4 "4 5 1 2 " 3 40 30 20 10 Mean = 0,3841 Std. Dev. = 0,34083 N = 193 0 -0,50 0,00 0,50 1,00 IAT Effect (D measure) / >3 = "4 3/ )GK 3 Linear Cubic 0,0 -0,1 -0,2 -0,3 -0,4 .00 .50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 Standardised IAT effect + 94 1 "4 F 3" M?3&23 4 ?3?>& H 3 F "4 > + ?3?K) "4 H 4 '" 34 21 / K3 = "4 3! )K& 3 Linear 0,00 Cubic -0,20 -0,40 -0,60 -0,80 -1,00 .00 .50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 Standardised IAT effect + 94 1 "4 F 3" M?3&23 4 ?3??) H 3 F "4 > + ?3?D) "4 H 4 '" 34 22 " 4 )3 - * & 3 !" 1 - 15 2 1 5 " C = " + 4 >?' DG >>) ) ?)' ) 'GJ / O2 D& 1K?2 )J 1K)2 &> 1K>2 D( 1)G2 )GK 1>&2 )J' DG )G> >G' (>G * K3& 1>3?2 >3G 1)3K2 K3> 1)3D2 )(3K 1)(3'2 < 1) 'GJ2 5 1 @ A + "4 3 / @ @ A3 4 >3 8* 3 )GK ! 5 ; 23 5 34 5 3 3 1K?O2 A 3 " " " ! ! + 94 4 ) 3 23 4 * K3 ! * " 3 )GK # $ %& ' ()* $ %- !. $ % - !. $ %1 !. / ! $"% 1 !. / ! $ %2 / ! ' $ % 2 / ! Note: * p<0.05. 4 # "4 3 " + ", $/ $/ 0 % 0 % ' $/ 4 0 % ) + + + + + + ", , , , + , + , + , + + , + , + , + , + , + + + , + , + , + , + ", + , + + + + , , , , + , + , + + + + ", + , + , + + + , + , + , + , 3 24 Table 4A. The correlation between the callback rate for interview and the implicit and explicit attitude and stereotype measures. Percentage points. Full data of 193 observations. 3 . ! // ! # 4 5 ! !. ! ) # 3 7 ) & !7 7 - + $ + % / / ! ). + $ + % ' + ,,, $ + % + $ + % + " $ + % / # / : < . 9 / + , % ' ! / 5 7 // 2 1 2 4 0 9 ; 7 91 + + $ + , % + $ + , % + $ + ; 9 + ",,, $ + " % + ",, $ + % + $ + % ; ; + ,, $ + " % % + " $ + "% + $ + + $ + + $ + 6 , % + ,, $ + " % + ,, $ + " % + ,,, $ + " % + ,, $ + % + $ + % + ,,, $ + " % + ",, $ + % + " $ + % ; ; + $ + " % % + " $ + % + $ + + $ + % + ,,, $ + % + $ + % + $ + % ; ; 9 ; + ,,, $ + % + $ + % + "" $ + % + ,,, $ + % + " $ + % + $ + % + ,,, $ + % + " $ + % + $ + "% ; 9 ; ; ; ; % % ; ; 38 54"4" G3 4 & )? 34 8 % 1 2 )GK ! + $ + ! 3 9 + $ + 6 !. 1 !. 2 7 8 3 7 ) ! 6 !7 3" 4 * ) * # C3 34 ) D )K& ?3?J ?3D' 3 25 4 'C3 4 3- + )GK 3/ * 3 3 . ! // ! # 4 5 ! !. ! ) # ! 3 7 ) $/ - 0 % !. / / ! $/ ! 9 : < . 9 / + / ' ! / 7 // $/ 0 % + ,,, $ + % + $ + % + $ + "% 91 + 2 1 2 4 0 9 ; 7 ; 9 + ", $ + % + " $ + % + $ + + $ + + , $ + "% % + $ + + ,,, $ + " % + ,, $ + % + , $ + % , % + $ + "% + ,,, $ + " % + ,, $ + % + , $ + % + ,,, $ + " % + ,, $ + % + , $ + % ; ; % + $ + % + ",,, $ + % + $ + % + " $ + % ; ; 1 2 9 ; + ", $ + % + ,,, $ + % + $ + % + $ + % ; 9 % + ,,, $ + % + " $ + % + $ + % ; ; ; ; + " $ + % + " $ + % + ,,, $ + % + $ + % + $ + % ; ; 38 3" ?3D' ,, % 6 + " $ + % + $ + + $ + ; ; 54"4" G3 4 ?3?J , % 0 % ' 5 + $ + % 8 + ", $ + % / # + $ + 6 0 % 3 ). 8 + $ + " % $/ 1 !. 2 + 3 7 ) * 4 ) 34 34 3 26 Table 4C. Interaction effects. Percentage points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ppendix 4 ")3 " 6 # A # 9 + $ % 6 / ! * $ !7 ! % 8 ! ! 2 * ) ! ! 9 * !7 ' * $ !. . % 6 ! ! 5 4 B ! 5 4 3 7 & ! * + 9 94 0 7 9 + $ % ) ! ! 9 + $ % " 7 * ! 9 + $ % : ! ' &5 7 !7 !. ! ! 7 9 + $"% : ! ' ) # !7 !. ! ! 7 9 + $ % " "" " " "" " " " C"" ! C " ) # &5 7 !7 !. !7 !. ! ! B $ ? "%>$ % $ ? %>$ % $&5 7 %>$) # % + + + +" + " + + " + + + + + + + + + + + + + + " + + " + + + + + + + " + + + + + + + + +" χ2 + + + ,,, + ,,, + + ,,, + ,, + ,,, + ,,, "+ ,, + ,,, + ,,, + ,,, 1>??(23 @C &3&K 1 9 (! 4 2 H K3J' 1 A 23 1 2 0 χ2 1D2 U 1&23 4 3 31 4 ">3 + N < "4 3 4 ) # >3 6 # 4 ! 3 9 # / &5 7 +" +" / !. +" + ' 5 + +" + + #+ + + + + + " + " + + + " % + + . % + + " + + + + + " + + + + + + + + $ + % + " , $ + % + $ + % + $ + % + $ + % + $ + % + " , $ + % + $ + % + $ + % + " $ + % + $ + % + " $ + % 3 8 4 ! ! 5 4 7 ! ! 2 * $ * $ !. * $ 6 ! !7 ' % ! !. 6 ) ! ! B ! 5 4 9 9 + ! + & 6 ! 9 + ! # 2 3 ! / ! 2 6 # 1?<) / + $ + % + ", $ + % + $ + % + $ + % " 9 4 3 4 * + 1 "4 F 23 2 3 32
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