The measurement of pay discrimination between job assignments

The traditional Becker/Arrow model of taste discrimination in pay depicts majority and minority labour as perfectly substitutable, implying that all workers perform precisely the same job assignment and have the same qualifications. The model is thus only appropriate for determining whether ceteris paribus pay differences between white workers and non-white workers, for example, performing job assignment A are attributable to prejudice ('within-assignment discrimination'). The model is inappropriate for determining whether ceteris paribus pay differences between white workers in assignment A and non-white workers in assignment B reflect prejudice ('cross-assignment discrimination'). We extend the traditional model to allow for cross-assignment discrimination and we propose an empirical methodology for its estimation. In so doing we address two broad questions: (1) Do predictions about cross-assignment discrimination vary with the form of the production function?; and (2) How can one estimate such discrimination when there is no common measure of productivity? We address the first question by deriving a measure of cross-assignment discrimination for four different production functions--Generalized Leontief, Quadratic, CES, and Cobb-Douglas. The Generalized Leontief provides the most general results, although closed form solutions are not possible. Closed form solutions are obtainable from the other three functions, but only under restrictive assumptions. There are two main findings. First, most predictions are generally robust across functional forms. Second, cross-assignment discrimination depends upon productivity and labour supply differences between the two worker groups, labour market structure, and the interaction between relative group productivity and prejudice. We address the second question by outlining, for future exploration, a two-stage regression methodology in which a standardised (i.e. common) measure of productivity is estimated separately for each occupation. This measure is then incorporated as a right-hand-side explanatory variable in a second-stage, all-occupation regression designed to estimate cross-assignment discrimination. We discuss the proposed methodology with reference to a valuable and interesting test case: The market for professional sports players.