Statistical Theories of Discrimination in Labor Markets Author(s): Dennis J. Aigner and Glen G. Cain Reviewed work(s): Source: Industrial and Labor Relations Review, Vol. 30, No. 2 (Jan., 1977), pp. 175-187 Published by: Cornell University, School of Industrial & Labor Relations Stable URL: http://www.jstor.org/stable/2522871 . Accessed: 24/02/2012 10:02 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. Cornell University, School of Industrial & Labor Relations is collaborating with JSTOR to digitize, preserve and extend access to Industrial and Labor Relations Review. http://www.jstor.org STATISTICAL THEORIES OF DISCRIMINATION IN LABOR MARKETS DENNIS J. AIGNER and GLEN G. CAIN E CONOMIC discrimination has been diffi- perspective suggested by Kenneth Arrow, cult to explain by means of standard John J. McCall, Edmund S. Phelps, Mel- neoclassical economic models that assume vin W. Reder, and A. Michael Spence, all pervasive competition. Why, after all, of whom focused on certain implications should two groups of workers who have of employer uncertainty about the produc- the same productivity receive different re- tivity of racial (or sex) groups of workers, muneration? The challenge to explain this particularly in the context of hiring and phenomenon is posed most sharply by the placement decisions., This paper offers marked differentials in wages and earnings several models that clarify the meaning of between blacks and whites and between economic "statistical discrimination," sim- men and women differentials that remain plify the theory, and yield plausible em- substantial despite diligent efforts to con- pirical implications. On the other hand, trol for supply-side productivity traits. the paper also identifies several shortcom- This paper examines that issue from a ings of "statistical discrimination" models; shows that the often-cited Phelps model does not constitute economic discrimina- Economic discrimination in labor markets is con- ventionally defined as the presence of different pay for workers of the same ability. This paper analyzes iKenneth Arrow, "Models of Job Discrimination" that problem with the aid of a simple stochastic and "Some Mathematical Models of Race in the model in which employers hire, place, anad pay Labor Market," in Anthony H. Pascal, ed., Racial workers on the basis of imperfect information about Discrimination in Econ omic Life (Lexington, Mass.: their abilities. The available information consists Lexington Books, D. C. Heath and Co., 1972), pp. of both group membership (black, white; male, fe- 83-102 and 187-204; and "The Theory of Discrimi- male) and information about individlual perform- nation," in Orley Ashenfelter and Albert Rees, eds., ance on some fallible indicator of ability (e.g., a Discrimination, in Labor Markets (Princeton, N. J.: test). Several types of economic discrimination with- Princeton University Press, 1973), pp. 3-33; John J. in the context of competitive market assumptions McCall, Inicomie Mobility, Racial Discrimination, are examined by means of several models, anid the and Economic Growth (Lexington, Mass.: Lexington empirical plausibility anad implications of these Books, D. C. Heath and Co., 1972); and "The models are discussed. The authors conclude that Simple Mathematics of Information, Job Search, the statistical theories are unlikely to provide an and Prejudices," in Anthony H. Pascal, ed., Racial important explanation of labor market discrimina- Discrinsination7 in Economic Life (Lexington, Mass.: tion uender conventional neoclassical assumptions. Lexington Books, D. C. Heath and Co., 1972), pp. Dennis J. Aigner and Glen G. Cain are both Pro- 205-44; Edmund S. Phelps, "The Statistical Theory fessors of Econormics at the University of Wvisconsin. of Racism and Sexism," Amierican Economiic Review, They express their gratitude for the extensive com- Vol. 62, No. 4 (September 1972), pp. 659-61; Melvin ments of Arthur S. Goldberger. This research was W. Reder, "HunmanCapital and Economic Discrimi- supported iln part by funds granted to the Institute nation," in Ivar Berg, ed., Hu-nman Resources and for Research on Poverty at the University of Wis- Economic Welfare; Essays in Honor of Eli Ginzberg consin-Madison by the Office of Economic Oppor- (New York: Columbia University Press, 1972), pp. tunity plursuant to the Econoomic Opportunity .-\ct 71-88; and A. Michael Spence, "Job Market Signal- of 1964 (GGC), and by NSF grant GS-30005 (DJA). ing," Quarterly Journal of Economics, Vol. 87, No. 3 The opinions expressed here are those of the (August 1973), pp. 355-74 and Market Signtaling au thors-EDITOR (Cambridge, Mass.: Harvard University Press, 1974). 175 176 INDUSTRIAL AND LABOR RELATIONS REVIEW tion, statistical or otherwise; and concludes By normal distribution theory, Equation that these models probably do not explain 2 is the least squares regression, expressing most labor market discrimination. q in terms of a group effect [(1 - .y)a] and an individual effect (yy). It is useful to think The Basic Model of Equation 2 as a conditional expectation We introduce the statistical model of from a linear population regression func- discrimination with the version by Phelps, tion: contained in an article with the imposing title, "The Statistical Theory of Racism (4) q = (1 -y)a + yy + u' and Sexism.'"'2 The essential features are where u' is the usual well-behaved error as follows. In the hiring and placement of term. In principle, the regression is opera- workers, employers base their decisions on tional, because employers could measure some indicator of skill, y, (such as a per- the actual q of a worker on the basis of a formance test) that measures the true skill post hoc evaluation of the worker's per- level, q. The terms "ability," "productiv- formance. ity," and "skill" will be used interchange- Now, consider two differentiated groups ably herein. In practice, y would un- of workers, say whites and blacks, with doubtedly involve a number of measures, possibly different means, aw and a B, and but the assumption here will be that a possibly different variances of q and u. single test score is all that is measured by (Although we use whites and blacks y. The measurement equation is throughout, our discussion is equally ap- plicable to males and females.) The em- (1) y = q + u, ployer is assumed to pay a worker an where u is a normally distributed error amount, q, based on the specific informa- term, independent of q, with zero mean tion available for each group and indi- and constant variance; q is also assumed vidual (see Equation 2): to be normally distributed with a mean equal to a and with a constant variance. (5a) qW= (I -yW ) W + WyW Employers can observe the test score, y, (5b) AB= (1 B)B + ByB. but they are interested in this only insofar as it gives them information about the The slope, y, will generally differ for the unobservable variable, q. Thus, the imme- two groups if the variances of q and u diate interest of the employer is the ex- differ, as shown by Equation 3.3 pected or predicted value of q, which we The nature of the hiring and placement shall label 97. process requires that the employer make a subjective assessment of a worker's skill. The expected value of q, given y (E(qjy)) is: We assume that this assessment of q, given y, will equal the expectation of q, condi- (2) q=E(q y) = (I - y) a + yy, tional on y. This assumption is in keeping with wage-maximizing behavior by work- where a is ithe group mean of q (and y) and 3Any random error in y as a measure of q is (3) ly Var(q) Cov(qy) represented by u. A systematic error in y as a meas- groups could Var(q) + Var(u) Var(y) tire of q for one or the other racial also be introduced, but this would not add substan- tively to our analysis. For example, if blacks scored = [ Cov(q,y)2 = r2] below whites by some constant amount for any q LVar(q) Va r(y) value, a negative intercept term could be added to where r2 is the squared coefficient of cor- Equation 1. However, a simple transformation in which this intercept difference was added to qB relation between q and y. In classical test would restore comparability in the q values for both score theory, y is the reliability of a test groups according to a new set of equations like score, y, as a measure of the true score, Equations 5a and 5b. This type of bias in the test q. Clearly, 0 < y < 1. instrument would not, by itself, affect the reliability of the instrument and is, therefore, inconsequential. The unreliability of y as a measure of q, however, 2American Economic Review (September 1972). is another matter, as we demonstrate later. STATISTICAL THEORIES OF DISCRIMINATION 177 ers and profit-maximizing behavior by em- interpret the "statistical theory of dis- ployers, since a job market function of crimination" as a theory of "erroneous" or employers is to assess (or predict) factor "mistaken" behavior by employers, as have productivity, given the costs of available some economists,6 is therefore without information, and to pay the factors of foundation. Furthermore, Andrew I. production accordingly. Employers who Kohen errs by claiming that, "Phelps are inefficient in this function will tend to [1972] demonstrates that irrespective of the be weeded out by the "market mecha- validity of using sex" as a proxy variable nism" of competition.