Measurement Error in Job Evaluation and the Gender Wage Gap
Chen, Shih-Neng, Orazem, Peter F., Matilla, J. Peter, Greig, Jeffrey J., Economic Inquiry
Wage equations are widely used to estimate the size of the pay gap between male- and female-dominated jobs. When jobs are the unit of observation, job wage rates are regressed on job attributes (such as skill, effort, responsibility, and working conditions) and on the percent of female incumbents in the job. The coefficient on the percent female variable estimates the size of the gender pay gap, which is often taken as a measure of pay discrimination against women.(1) These estimates frequently become the metric for upward adjustment of female-dominated job pay to redress the discrimination. Summarizing the research which uses jobs as the unit of observation, Ehrenberg  concluded that female-dominated jobs are underpaid by 15%-34% relative to male-dominated jobs. Similar findings have been reported in studies which use individuals instead of jobs as the unit of observation.
Many criticisms have been raised of these two types of studies. One common criticism is that not all relevant control variables for job attributes or individual productivity may be measured (or even measurable) so that specification error arises. If these omitted variables are correlated with the gender variable, then the estimated gender pay gap incorporates legitimate differences in productivity and/or job attributes. However, few studies have analyzed the impact of omitted factors bias empirically.
Another common criticism is that there is measurement error in the control variables which in turn leads to biases in estimating the size of the pay gap. Measured job attributes are highly subjective in nature, making measurement error a major problem. Even human capital measures of education and training are subject to error. Although one may easily measure years of completed education and experience, it is much more difficult to measure years of effective learning or achievement. Only a few studies have analyzed the size of these biases empirically.
This paper provides the first estimates of the size of this measurement error bias in the context of job level (job attribute) wage equations. To our knowledge, only two previous studies have estimated measurement error bias using individual level, human capital wage equations, and both are tangential to the major question that we address.
In particular, we find that the estimated gender pay gap is overstated by 34%-44% when measurement error bias is ignored in job level wage equation analysis. Wage adjustments to correct the gender gap in pay which adhere strictly to such biased estimates may lead to millions of dollars in over-compensation. In the future, job evaluation should correct for this bias and we suggest appropriate procedures. In addition, we provide unique evidence that previous attempts to add measures of seemingly "omitted" job attributes need not have reduced the bias in the measured pay gap. We find that the number of job attributes which enter the wage regression is artificially increased because measurement errors reduce the measured collinearity among job factors.
The next section explains factor-point pay plans and summarizes the few related studies. Section III reviews the statistical theory of regression analysis when there is measurement error in the explanatory variables. We analyze the effect of independent and correlated measurement errors between job factors on the estimated magnitude of pay discrimination. Section IV discusses the data and reports the empirical results from implementing various measurement error corrections. The final section summarizes our findings and suggests how this study could be used to improve future factor-point pay analysis.
II. BACKGROUND AND RELATED RESEARCH
More than half of the workers in the United States are paid according to a pay system at least partly based on job evaluation. These systems establish hierarchies of jobs and pay levels using information on a common set of job attributes such as skill, effort, responsibility, and working conditions. …