Local Linear Peters-Belson Regression and its Applications to Employment Discrimination Cases Open Access
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In discrimination cases concerning equal pay, the Peters-Belson (PB) regression method is used to estimate the pay disparities between minority and majority employees after accounting for major covariates (e.g., seniority, education). Unlike the standard approach, which uses a dummy variable to indicate protected group status, the PB method first fits a linear regression model for the majority group. The resulting regression equation is then used to predict the salary of each minority employee by using their individual covariates in the equation. The difference between the actual and the predicted salaries of each minority employee estimates the pay differential for that minority employee, which takes into account legitimate job-related factors. The average difference estimates a measure of pay disparity. In practice, however, a linear regression model may not be sufficient to capture the actual pay-setting practices of the employer. Therefore, we use a locally weighted regression model in the PB approach as a specific functional form of the relationship between pay and relevant covariates is no longer needed. The statistical properties of the new procedure are developed and compared to those of the standard methods. The method also extends to the case with a binary (1-0) response, e.g., hiring or promotion. Both simulation studies and re-analysis of actual data show that, in general, the locally weighted PB regression method reflects the true mean function more accurately than the linear model, especially when the true function is not a linear or logit (for a 1-0 response) model. Moreover, only a small loss of efficiency is incurred when the true relation follows a linear or logit model.