identical then we could give the treatment to only one of the two individuals

# Identical then we could give the treatment to only

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identical, then we could give the treatment to only one of the two individuals and compare the values obtained. Usually, we cannot make these assumptions in social sciences. However, if instead of studying the treatment effect, we rather look at the average treatment effect, we would be able to overcome the confounding variable problem under the assumption of ignorability. The average treatment effect is T = E [ Y t ] - E [ Y c ] but we only observe T = E [ Y t | P = t ] - E [ Y c | P = c ] where P denotes the value of the treatment attributed to individuals. Then under the assumption that Y t , Y c P , i.e. the treatment is attributed at random, 11 we finally have that E [ Y t | P = t ] = E [ Y t ] which solves the problem. 2.2 Segregation and causality The ignorability assumption is crucial for causal inference. However, in the case of residential segregation, we cannot use this approach for several reasons. First, 10 Holland[28] discusses at length this problem. 11 If there is other covariates in the model explaining the value of interest, the ignorability assumption is recast as Y t , Y c P | X 5
residential segregation suffers from reverse causality. For instance, does an increase in crime cause more segregation or is it the reverse? It could be that individuals move if the level of criminality increases because they are risk averse. 12 Criminal- ity might rise in more diverse areas because of the tensions associated with the interactions of the different groups. 13 Or it might be that segregation, by limiting the opportunities of the minority group, shift downward the opportunity cost for engaging in criminal activities, thus raising the criminality in the area. 14 The second reason is the difficulty to find simultaneously an exogenous variation for all the potential determinants of segregation. In our context, it would mean finding simultaneously an exogenous income shock and an exogenous criminality shock (in the hypothesis that segregation is only caused by criminality and income) at the subplace level in South Africa in the period 1996-2011, which seems (almost) impossible. At least to the best of my knowledge, there are not such data. However, we can disentangle the problem of causality by looking at the differ- ent potential determinants. But first, we must acknowledge the fact that causality is limited by the state of our knowledge at the moment of the analysis. Thus a variable might not be considered as a cause before some (robust) confirmatory evidences, or a cause might be revoked by (robust) dissenting evidences. For in- stances, smoking cigarettes was associated with lung cancers only at the beginning of the 20th century, 15 while hysteria was believed to be the consequence of women menstruations until 1980. 16 For residential segregation, we actually know that a lot of variables are candi- date for causing segregation. 17 We can actually divide the different theories into three groups labelled Place stratification , Spatial assimilation , and Income sorting .

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