Upward and Downward Bias When Measuring Inequality of Opportunity

Abstract

We show that, when measuring inequality of opportunity with survey data, scholars face two types of biases. A well-known downward-bias, due to partial observability of circumstances that affect individual outcome, and an upward bias, which is the consequence of sampling variance. The magnitude of the latter distortion depends on both the empirical strategy used and the observed sample. We suggest that, although usually neglected in empirical contributions, the upward bias may be significant. We propose a simple criterion to select the best specification which balances between the two sources of bias. Our method is based on cross validation and can be easily implemented to survey data. In order to show how this method can improve our understanding of the inequality of opportunity measurement, we provide an empirical illustration based on income data of 26 European countries. Our evidence shows that estimates of inequality of opportunity are extremely sensitive to model selection. Alternative specifications lead to significant differences in the absolute level of inequality of opportunity and to a number of substantial countries' re-ranking. This in turn clarifies the need of an objective criterion to select the best econometric model when measuring inequality of opportunity.

Inequality of opportunity in an outermost region: the case of the Canary Islands

“…Focusing on the MLD, IO in the Canary Islands represents 12.4% of total inequality, while the Theil 1 and Gini indices are 13.2% and 37.8%, respectively (Model 4). Consistent with Brunori et al (2016), the MLD (and Theil 1) is notably lower than the Gini index. Taking as a reference the estimates of European and Latin American countries using the same procedure (Ferreira & Gignoux, 2011;Marrero & Rodríguez, 2012), the MLD IO ratio found for the Canary Islands archipelago is similar to the value of Spain and countries such as Ireland and France but higher than those of the Northern Countries and Central Europe (with the exception of Belgium), and lower than those of Latin American countries, which reach 20% on average.…”

“…The within-group inequality component contains non-observed circumstances, luck, and other measurement errors, which prevent us from considering this measure as a proxy for inequality due to individual effort. For illustrative purposes, we also include the Theil index (T 1 ), which belongs to the Generalized Entropy index class and is therefore additively separable (Bourguignon, 1979), and the Gini index, which despite not being additively decomposable, is the most used index to measure total inequality, and its between-group component can be considered as a proxy for IO (Brunori et al, 2016). See Ferreira and Guignoux (2011) and Marrero and Rodriguez (2012) for a technical description of the methodology.…”

“…Their outermost region status makes the Canary Islands a significant case for the study of the Inequality of Opportunity (IO) because, although institutions in the archipelago are comparable to those in the rest of Spain, the islands have an income per inhabitant that is 82% index and, for illustrative reasons, we also consider the Theil and Gini indexes (Brunori et al, 2016). This analysis is carried out on different models according to the type of circumstances considered and for certain relevant groups of islands.…”

The Evolution of Inequality of Opportunity in Germany: A Machine Learning Approach

“…The first step to estimate both equation 4and equation 6is the identification of circumstances beyond individual control that define types. 4 The selection of circumstances is a key aspect of any empirical analysis of IOP because estimates have been shown to be sensitive to the number of types considered (Brunori et al, 2018b;Ferreira and Gignoux, 2011;Rodríguez, 2008).…”

“…the need to assume how these circumstances interact with effort in determining individual outcomes. Both choices have been shown to crucially affect the estimated level of inequality of opportunity (Brunori et al, 2018b).…”