9. Variance Function Regressions for Studying Inequality

Abstract

Regression-based studies of inequality model only between-group differences, yet often these differences are far exceeded by residual inequality. Residual inequality is usually attributed to measurement error or the influence of unobserved characteristics. We present a regression that includes covariates for both the mean and variance of a dependent variable. In this model, the residual variance is treated as a target for analysis. In analyses of inequality, the residual variance might be interpreted as measuring risk or insecurity. Variance function regressions are illustrated in an analysis of panel data on earnings among released prisoners in the National Longitudinal Survey of Youth. We extend the model to a decomposition analysis, relating the change in inequality to compositional changes in the population and changes in coefficients for the mean and variance. The decomposition is applied to the trend in US earnings inequality among male workers, 1970 to 2005.

Race‐based job discrimination, disparities in job control, and their joint effects on health

“…Methods are outlined by Western and Bloome [2009] and entail an iterative set of gamma regressions (using a log link) of the squared residuals from each linear regression model on the covariates that were included in the model. The resultant coefficient describes the degree to which withingroup (as opposed to between-group) heterogeneity contributes to inequality, and assists in discerning or discovering omitted variables, or the influence of an included factor.…”

Wage Inequality Within and Between Occupations

“…The most attractive feature of variance of log wages for this research, though, is that it can be decomposed into within-and between-occupation inequality (Allison, 1978). The analytical approach is based on the framework for studying inequality suggested by Western and Bloome (2009) and similar to that used in previous empirical research on this topic (Mouw & Kalleberg, 2010;Williams, 2013). The analysis consists of three steps.…”

A spatial hedonic model application of variance function regression to residential property prices in Beijing

“…The purpose of this paper is to provide a description and application of a type of aspatial individual residual analysis that can be used to further explore the results from spatial models. The analytical approach, as described below, is called variance function regression (Western and Bloome 2009).…”