Beyond Gender: A Logistic Ordinal Regression Model for Earnings Differences

EXECUTIVE SUMMARY How important is gender in predicting an individual's personal earnings? The hotly-debated "gender gap" suggests that women do not earn as much as men for equal work. This work develops two multiple logistic ordinal regression models that measure the effect of job and personal characteristics on personal earnings of salaried and hourly-wage workers in the Maine labor force. The models produced not only exhibit substantial predictive accuracy, but also begin to unwind the complex effects that factors such as education, industry, location, and unionization have on what one makes. Keywords: Earnings Survey, Gender Gap, Logistic Ordinal Regression INTRODUCTION Gender is often cited as the explanation for gaps in earnings regardless of industry, location, tenure in the job, and other factors. This study identifies significant drivers of hourly wages and salaries for Maine workers using data from a study that analyzed Maine's labor force, and paints a much more complex picture. It applies logistic ordinal regression (LOR) to build individual earnings models for both salaried and wage-earning men and women. These models are then used to simultaneously examine the effects on the earnings of Maine workers' personal characteristics, such as the region where the individual lives, and job characteristics, such as industry choice. Most of the previous research involving the modeling of human capital uses ordinary least squares regression analysis. However, earnings data are rarely collected using exact dollar amounts. Even the U.S. Census uses earnings bands, as people are more likely to respond if presented with ranges of possible responses. Unfortunately, two major statistical assumptions of least squares regression are violated when a dependent variable, such as earnings, is recorded in bands. First, the variance of the modeled error terms cannot be constant, and, in fact, will vary as a function of the dependent variable. Second, because the dependent variable can only take on a limited number of values, the distribution of the error terms cannot be normally distributed. Under these conditions, the appropriate statistical tool is multiple logistic ordinal regression (MLOR), which can accommodate independent variables measured on a ratio, interval, ordinal, or nominal level. MLOR has been used for a variety of modeling purposes such as estimating, workplace satisfaction (Bennett, Robson, & Bratton, 2001), voter preferences (Koop & Poirier, 1994), and financial risk (Hawley & Fujii, 1994). This study compares the important drivers of personal earnings for two distinct groups: salary earners and hourly-wage earners. Survey data were drawn from respondents who were asked to report their earnings using standardized wage and salary bands. These bands were then used as the dependent variable in two multiple logistic ordinal regression models that explored the predictive value of a variety of independent variables describing personal-earner characteristics and job characteristics. Both of the resulting models show an impressive degree of accuracy in predicting wages, explaining 44.5 percent of the overall variability in salary bands and 48.7% of the variability in wage bands. More importantly, the models demonstrate that gender is but one of many considerations that influence earnings and is by no means the dominant one. MOTIVATION FOR THE STUDY The United States 2000 Census identified a significant but shrinking gap between the average earnings of men and women. Nationwide, the median income was reported as $18,957 for females and $29,458 for males, a gender earnings gap of $10,504. A substantial gender earnings gap was also documented in Maine, where the Census identified a $9,902 differential based on median male earnings of $26,546 and median female earnings of $16,644. A similar gap was reported by Seguino and Butler (1998), who calculated that in 1989 the median income for males in Maine exceeded the median for females by $9,818. …