Segregation and the Spatial Externalities of Inequality: A Theory of Interdependence and Public Goods in Cities – CORRIGENDUM

The author regrets that Xu (2023) contains an error in the first paragraph of the section “Estimation Strategy.” In describing the estimation strategy, Equations 2 and 3 are incomplete and the text that follows states: “where the instrument, $ {Z}_c $ , is the interaction of the predicted in-migration SSIV with a measure of “uphillness” of the city ( $ {\widehat{M}}_{c,t}\cdot {h}_c $ ). In the first-stage, I instrument for the socioeconomic segregation of each municipality c. In the second-stage, we observe the effects of segregation, predicted by the instrument, on the survey responses measuring preferences and the mechanisms.”

The corrected equations for the estimation strategy and the corrected text that discusses them are provided below:

First Stage IV:

(2) $$ \begin{array}{rl}{\mathrm{Seg}}_c=\gamma +\delta {Z}_c+{\unicode{x1D54F}}_c^{\prime}\mu +\sigma {\widehat{M}}_{c,t}+\tau {h}_c+{\epsilon}_c& \end{array} $$

Second Stage:

(3) $$ \begin{array}{rl}{\overline{y}}_c=\alpha +\beta \hskip0.3em {\mathrm{Seg}}_c+{\unicode{x1D54F}}_c^{\prime}\hskip0.3em \Gamma +\omega {\widehat{M}}_{c,t}+\psi {h}_c+{\varepsilon}_c.& \end{array} $$

The corrected text after the equations should read: “where the instrument, $ {Z}_c $ , is the interaction of the predicted in-migration SSIV with a measure of the mean “uphillness” of the city ( $ {\widehat{M}}_{c,t}\cdot {h}_c $ ). In the first-stage, I instrument for the socioeconomic segregation of each municipality c, while controlling for the two separate components of the instrumental variable: $ {\widehat{M}}_c,t $ and $ {h}_c $ . ¹ In the second-stage, we observe the effect of segregation, predicted by the instrument, on the average level of outcomes ( $ {\overline{y}}_c $ ), such as public goods provision or on survey responses measuring preferences and the mechanisms.” The corrected text also includes the addition of Footnote 1 below.

Thus, while the estimates in all the results tables remain correct, the main-text discussion erroneously omitted this clarification regarding the inclusion of these two separate components of the instrumental variable as control variables in the two-stage least squares (2SLS) estimation in Table 3.

In addition, Footnote 6 on page 4 states that: “Judgements based on morality of character are absent in the claim that slums are a source of crime.” This footnote should have read: “This is not to attribute agency on the part of poorer communities as being the source of negative externalities. Historically, the status of informality of these “slum” settlements resulted in the absence of the state in these territories and, in turn, the deprivation of basic urban services. This chronic deprivation, this informality, is the source of the externality.”