Previous estimates of unfair inequality of opportunity (IOp) are only lower bounds because of the unobservability of the full set of endowed circumstances beyond the sphere of individual responsibility. In this paper, we suggest a new estimator based on a fixed effects panel model which additionally allows identifying an upper bound. We illustrate our approach by comparing Germany and the US based on harmonized micro data. We find significant and robust differences between lower and upper bound estimates - both for gross and net earnings based either on periodical or permanent income - for both countries. We discuss the cross-country differences and similarities in IOp in the light of differences in social mobility and persistence.