Selection bias and measures of inequality

Variables typically used to measure inequality (e.g., wage earnings, household income or expenditure), are often plagued by nonrandom item nonresponse. Ignoring non-respondents or making (often untestable) assumptions on the nonresponse sub-population can lead to selection bias on estimates of inequality. This paper draws on the approach by Manski (1989,1994) to derive bounding intervals on both the Gini coefficient and the Inter-Quartile range. Both sets of bounds provide alternative measures of inequality which allow for any type of selective nonresponse, while making no assumptions on the behaviour of non-respondents. The theory is illustrated measuring earnings inequality (over time and between samples) for post-unification Germany over the nineties.