share of total inequality that is related to the inequality due to differences in circumstances is interpreted as the IOO.

Unfortunately, this empirical strategy suffers from a drawback: it provides at best lower bounds of the true IOO. One well-recognized factor leading to this downward bias is that only a subset of all relevant circumstances are observable in available datasets (Ferreira and Gignoux, 2011). The imprecision in measurement of the outcome variable is another reason recently pointed out by Chavez-Juarez (2015).

An additional factor possibly adding to the downward bias of IOO estimates is the lack of information about a portion of the population under study. Available data are usually gathered through surveys that likely do not reach the most favored population. If this is the case, sample distributions of outcome variables miss the rightmost section of the right tail of the population distribution. Thus sample distributions of outcome variables erroneously look more homogeneous than the true population distribution. Downward bias in IOO estimates is then a consequence of the smaller variation in the sample distribution. The magnitude of the downward bias depends on how much variation is lost. Loss in variation is likely large because most favored individuals usually reach large outcome values.<sup>5</sup> The possible additional bias from not observing top income populations has largely been overlooked in the IOO literature.<sup>6</sup> For instance, Roemer and Trannoy (2013) provide a lengthy, thorough discussion on the limitations stemming from poor quality data. They emphasize on the need of improving survey, particularly in developing countries. They point out the relevance of gathering physical information such as body mass index and psychological information such as mental health indicators and IQ measures. They also highlight how important is to measure achievements of children around the age of consent. But these recommendations aim to improve the gathering of circumstances, overlooking the possible consequences of not observing subpopulations at all.

In this context, a question with very practical implications naturally arises: is there a way to quantify the downward bias of IOO estimates? This paper answers this question by means of Monte Carlo simulations that experimentally manipulate three factors: i) not observing most favored populations; ii) not observing all relevant circumstances; and iii) interaction between not observing neither most favored population and all relevant circumstances.

> 5 The issue on information about the most favored population not being available in household survey datasets has been discussed before in studies of inequality of outcomes (e.g. Korinek et al. (2006) for the case of the U.S., and Hlasny and Verme (2013) for the case of Egypt) but its implications for the estimation of IOO measures has been overlooked so far.

> 6 As part of a companion project, we study the impact of an additional empirical issue –living standards across regions. So far, researchers focusing on income or wages have overlooked differences in costs of living across regions of a country. As a consequence, total inequality in income is likely to be overestimated. This is the case because high income individuals usually live in locations with higher costs of living than low income individuals. By not adjusting for differences in purchasing power, high income individuals appear richer than they actually are. Ongoing research is focusing on i) the implications of not adjusting for purchase power on IOO estimates, and ii) the impact of not observing the most favored population on IOO estimates in this context. Implications on the estimation of Growth Incidence Curves from not adjusting for purchase power has been discussed in other studies (e.g. Skoufias and Olivieri, 2013) but it is an overlooked issue in the IOO literature.

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