"This study analyzes the extent of downward bias in the calculation of inequality of opportunity for continuous outcomes such as income. A typically recognized source of bias is the unobserved circumstances as there is a limited set of variables available in household and labor force surveys. Another previously overlooked source is the likely unobservable nature of top incomes. Using Monte Carlo simulations where the underlying inequality of opportunity is predetermined at various levels, the study presents three key findings. First, the omission of a relevant circumstance can bias the inequality of opportunity estimate by as much as 80 percent, depending on how much variation of the outcome such circumstance explains. Second, not observing the top 5 percent of the income distribution can lead to downward biases of anywhere between 12 and 35 percent, and the combination of missing the most favored population and even one relevant circumstance exacerbates the bias of the empirical estimates. The third key result is that the estimated inequality of opportunity is strongly correlated with the amount of variation in the outcome variable explained by the combination of circumstances (measured by the R2). This result suggests that in empirical applications, the inequality of opportunity estimate can be roughly (and quickly) approximated using simple econometric techniques."

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