Delores A. Conway

Reverse Regression, Fairness, and Employment Discrimination

Possible salary discrimination can be studied by comparing mean salaries of, say, males and females, after statistical adjustment for differences in job qualifications. The adjustment is often made by regression, with salary as dependent variable, and job qualifications and sex as independent variables. One might also regress job qualifications on salary and sex, a procedure called reverse regression. Ideas about fairness as well as technical concepts are relevant to discrimination studies. There are two distinct aspects of fairness, one based on comparisons of salary and the other based on comparisons of qualifications. Both concepts are needed to evaluate fairness.

Stable Factors in Security Returns: Identification Using Cross-Validation

Recent papers in financial research focus on identifying a stable factor structure for security returns. The likelihood ratio test typically is used to determine the number of factors from exploratory factor analysis models. In this article, we consider the use of cross-validation to identify a stable factor structure in security returns. When applied to actual stock-return data, cross-validation identifies a smaller number of stable factors than the likelihood ratio test. In groups of 30–60 randomly selected securities, cross-validation suggests one dominant factor, whereas the likelihood ratio test identifies from four to six factors. Furthermore, when groups are designed to highlight industry or size effects, the discovery of more than one dominant factor is problematic. Even if there are multiple economic factors generating stock returns, they may be difficult to disentangle if the underlying factors tend to be correlated.

Rejoinder to Comments on "Reverse Regression, Fairness, and Employment Discrimination."

1. The effects of bringing in additional data upon tentative conclusions about fairness 1 and fairness 2 (Ferber and Green). 2. The appropriateness of direct and reverse regression for causal modeling of employer behavior (Goldberger). 3. The mathematical relationships between direct and reverse regression outcomes and consistency with fair employment practices (Greene and Miller). 4. The role of traditional economic theory about productivity and wage determination (Michelson and Blattenberger).

Analysis of employment discrimination through homogeneous job groups

Abstract In legal studies of employment discrimination, regression models are often used to evaluate possible salary discrimination. Potential confounding arises when the data represent a heterogeneous work force. The estimated salary differences from the regression model may be confounded with nondiscriminatory differences in salaries across jobs. One way to avoid this confounding is to estimate the regressions within relatively homogeneous job groups. The usual objection to conditioning on homogeneous jobs is that employers influence the selection of employees for jobs, which may itself be discriminatory. This objection can be met by separate study of the placement process. We consider a two-stage approach that focusses attention on definition of homogeneous job groups and corresponding candidate pools to study both salary and placement discrimination.

The maximum entropy moment matrix with missing values

Abstract The occurrence of missing values for one or several variables has the effect of adding a ridge along the diagonal of their maximum entropy (ME) covariance matrix. This is a second ridge in addition to the usual ridge of the ME covariance matrix.

The conditioning of the maximum entropy covariance matrix and its inverse

The maximum entropy covariance matrix is positive definite even when the number of variables p exceeds the sample size n. However, the inverse of this matrix can have stability problems when p is close to n, although these problems tend to disappear as p increases beyond n. We analyze such problems using the variance of the latent roots in a particular metric as a condition number.