Exploring the Sources of Downward and Upward Biases in Measuring Inequality of Opportunity

This study analyzes the extent of biases that affect the calculation of inequality of opportunity (IOO) for monetary outcomes such as income or consumption. Besides the largely recognized bias from unobserved circumstances, we explore two previously overlooked sources of bias: the unobservable nature of top incomes in household surveys, and the differences in costs of living. Using Monte Carlo simulations where the true IOO is known, this study presents four key findings. First, omitting a relevant circumstance can substantially downward bias the IOO estimate, and this bias is correlated with the variation of the outcome explained by the missing circumstance. Second, missing the top of the income distribution exacerbates the downward bias from omission of circumstances. Third, the IOO estimate is strongly correlated with the variation of the outcome variable explained by the set of observed combination of circumstances. This result suggests that the IOO estimate can be approximated using simple econometric techniques –such as OLS. Finally, misrepresenting differential costs of living as circumstances can lead to upward bias in the estimation of IOO, thus raising caution on the current practice of interpreting IOO estimates as lower bounds of the true IOO.