The dynamic structure is crucial to identify causal effects and it is not

# The dynamic structure is crucial to identify causal

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The dynamic structure is crucial to identify causal effects, and it is not specific to the study of segregation. Here, we have a general identification result as long as this kind of dynamic causal structure can be established. Theorem 1. If the relation between a cause and its determinants can be expressed as a dynamic autoregressive structure of order 1 with no contemporaneous correla- tions, then, by conditioning on all its determinants at the previous period, a causal effect is identified, and correlation is thus causation. The proof of this theorem comes from the observation that a path with a com- mon consequence has always also either a chain of mediation or a common cause with a determinant at the previous period as a middle variable. 30 Otherwise, the 30 Note the similarity between this theorem and the classical results on the omission of relevant regressors in the econometrics literature. The theorem is equivalent to saying that no relevant regressors are missing for the analysis of the model. 11
initial and final variables are not connected by a path because there is no contem- poraneous correlations. So, to connect the two variables, there always is a chain of mediation or a common cause which will be between the common consequence and the final variable. Then, we always can condition on a determinant at the previous period to block back-door paths containing common consequences. Thus, by con- ditioning on all the determinants at the previous period, we block all back-door paths, thus proving the theorem. So, applied to our study of the determinants of segregation, if we can control for differences at the previous period in crime rates, segregation levels, access to public goods, sociodemographic characteristics, and income levels, then we will be able to estimate causal effects of each determinant. 3 Methodology 3.1 Segregation curves Segregation curves are close parents of the Lorenz curve used for income inequal- ities. They both belong to the family of concentration curves. 31 They are con- structed by sorting census tracts 32 by the proportion of Blacks. 33 Then, the cumu- lative distribution of Blacks and Whites are computed on this ranking. 34 Finally, each point of the segregation curve S ( i ) until the i-th location, is constructed as: S ( { F B ( i ); F W ( i ) } ) = { ( F B (1); F W (1)); ( F B (2); F W (2)) ... ( F B ( i ); F W ( i )) } (1) Like Lorenz curves, they start at the origin (0;0) and end at the point (1;1). Segregation curves are important in that researchers can derive any segregation index measuring unevenness directly from them. For example, the Dissimilarity index is the maximum vertical distance between the segregation curve and the 45- degree line (representing perfect integration). The Gini index is the area between the segregation curve and the 45-degree line. 35 Segregation curves are not exempt from drawbacks. They only account for an unequal repartitions of individuals across a particular set of demarcations. Thus 31 See Hutchens[29].

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