Then by adding sequentially sets of covariates along all the possible sequences

# Then by adding sequentially sets of covariates along

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Then, by adding sequentially sets of covariates along all the possible sequences, we can recover the causal contributions of each of the determinants of residential segregation. We do not limit our analysis to the decomposition of the mean levels of seg- regation. This allows us to identify precisely which neighborhoods are essentially affected by a change in a particular covariate. For instance, we find that the basic characteristics of a dwelling (surface, number of rooms...) have only an impact for neighborhoods already experiencing some intermediate levels of integration, while sociodemographic characteristics only matter for almost completely Black neigh- borhoods. This brings nuances to the work of Bayer et al.[4]. From our findings sociodemographic characteristics matter only for a small share of neighborhoods. Moreover, when it matters, it accounts for around 25% only. Finally, our results seems to point toward the provision of public services as the main source of segre- gation. The paper proceeds as follow: section 2 describes our identification strategy of causal effects. Then we detail our method for the detailed decomposition of segregation curves in the next section. A presentation of the data is then provided in section 4. Finally, we discuss our results and their implications in the last section. 6 See Duncan and Duncan[21], Massey and Denton[35], and Hutchens[29] for a complete overview of segregation curves. 3
2 ”Correlation is not causation” versus ”No smoke without fire” 2.1 General approach to causal inference Empirical researchers are usually interested in causal questions such as ”Does X cause Y?” and if so the following natural question ”By how much does X change Y?”. Decomposition analyses consider mainly the second question while leaving the first question unsettled. Thus, most decomposition studies are simply descrip- tive and do not draw much attention on inference and causality questions. But answering the question of causality is not a simple problem, and most of the time the decomposition analysis is already interesting on his own. But if we want to further understand complex social phenomena such as residential segregation some causal inference has to be made. The problem of causal inference is that we usually cannot be sure, when two variables X and Y correlate, if this is truly a causal relationship. 7 It might be because the causal relationship is interpreted in the wrong direction, X does not cause Y but Y does cause X. Or it might be that a third unobserved variable Z is causing both. Or it might simply be randomness. 8 When interpreting the correlation between X and Y, we usually have a model in mind such as quantitative easing will generate inflation or the consumption of a household will increase if its income raises. If only one direction is possible to explain the correlation between the two variables, then the problem of reverse causality is avoided. In the previous examples, quantitative easing might be im-

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