Overlapping Jurisdictions & Residential Segregation by Race

class: center, middle, inverse, title-slide

.title[
# Overlapping Jurisdictions & Residential Segregation by Race
]
.author[
### Christopher B. Goodman, PhD </br> <svg viewBox="0 0 512 512" style="height:1em;position:relative;display:inline-block;top:.1em;fill:#333333;" xmlns="http://www.w3.org/2000/svg"> <path d="M459.37 151.716c.325 4.548.325 9.097.325 13.645 0 138.72-105.583 298.558-298.558 298.558-59.452 0-114.68-17.219-161.137-47.106 8.447.974 16.568 1.299 25.34 1.299 49.055 0 94.213-16.568 130.274-44.832-46.132-.975-84.792-31.188-98.112-72.772 6.498.974 12.995 1.624 19.818 1.624 9.421 0 18.843-1.3 27.614-3.573-48.081-9.747-84.143-51.98-84.143-102.985v-1.299c13.969 7.797 30.214 12.67 47.431 13.319-28.264-18.843-46.781-51.005-46.781-87.391 0-19.492 5.197-37.36 14.294-52.954 51.655 63.675 129.3 105.258 216.365 109.807-1.624-7.797-2.599-15.918-2.599-24.04 0-57.828 46.782-104.934 104.934-104.934 30.213 0 57.502 12.67 76.67 33.137 23.715-4.548 46.456-13.32 66.599-25.34-7.798 24.366-24.366 44.833-46.132 57.827 21.117-2.273 41.584-8.122 60.426-16.243-14.292 20.791-32.161 39.308-52.628 54.253z"></path></svg> <span class="citation">@cbgoodman</span>
]
.institute[
### <br/>School of Public & Global Affairs
]

---

class: middle, center

.font150[Do overlapping local governments further segregate metropolitan areas?]

---

## Reasons for segregation

.font120[
1. Individual preferences
2. Income sorting
3. Local government policy
]

---

## Local government policy → segregation

- Following Trounstine (2018, 2020), residents use restrictive land use regulations to limit housing production
- They do so to,
  - Maximize house prices
  - Minimize tax burdens
  - Ensure high quality public services
- This has the effect of reinforcing segregation

---

## Overlapping governments

- Commonly, special districts 
  - Administratively and fiscally independent from other local governments
  - Typically provide a single service (*specialization*)
  - Can choose their boundaries (*territorial flexibility*)
- Measured as the ratio of special districts to non-overlapping general-purpose local governments

---

## How do overlapping governments help segregate metropolitan areas?

- In light of "imperfectly restrictive" land use regulations, special districts can achieve much of what municipalities can
  - Specialized service provision can provide high quality public services
  - Such public services capitalized positively into house prices
  - By limiting service provision to within (homogenous) district, between parcel subsidies are minimized, keeping tax burden low
- Overlapping governments can mimic restrictive land use regulations
- Conditioned on residents having the knowledge to create special districts
  - Patterns of political involvement (white, male, homeowners) suggest the knowledge exists

---

## Sample construction

- Period: Census years, 1980 - 2010
- Units: SMSAs (1983 definition)
  - 309 PMSAs & NECTAs
  - To ensure outward growth of MSA does not influence results
- Data: Census of Population & Housing; Census of Governments
  - Tract level data normalized to 2010 definitions using the Longitudinal Tract Database

---
class: top, center

---

## Measuring segregation

Theil (1972) index based on entropy,
`$$E = \sum_{r=1}^R (\pi_r)\text{ln} \frac{1}{\pi_r}$$`
Where `$\pi_r$` is the proportion of racial group `$r$`

Segregation is measured as the deviation of `$E$` from a larger geographic aggregation of `$E$`, weighted by population.
`$$\begin{split}
H_{c{\_}t} & = \sum_{t=1}^T \frac{P_t}{P_c} \left( \frac{E_c - E_t}{E_c} \right) \\
H_{m{\_}c} & = \sum_{c=1}^C \frac{P_c}{P_m} \left( \frac{E_m - E_c}{E_m} \right)
\end{split}$$`

---

## Measuring segregation

As explained by Trounstine (2018), Theil's `$H$` index, calculated as the deviation of neighborhood diversity from metropolitan diversity, can be decomposed into the deviation between cities `$(H_{m{\_}c})$` and a weighted average of within-city deviations.

`$$H_{m{\_}t} = \sum_{t=1}^T \frac{P_t}{P_m} \left( \frac{E_m - E_t}{E_m} \right) = H_{m{\_}c} +\sum_{c=1}^C \left( \frac{P_c}{P_m} \right) \left( \frac{E_c}{E_m} \right) H_{c{\_}t}$$`

Overall `$(H_{m{\_}t})$` and between-city `$(H_{m{\_}c})$` segregation form the two dependent variables for this analysis.

---

## Identification strategy
<br />

`$$\begin{split}
SEG_{it} & = \beta_{ij} + \beta_2 DEMO_{it} + \beta_3 RHET_{it} + \beta_4 DENSITY_{it} + \beta_5 GROW_{it} \\ 
& + \beta_6 \widehat{OVERLAP}_{it} + \phi_i + \tau_t + \varepsilon_{it} 
\end{split}$$`

- `$DEMO_{it}$` = Black-white demographic characteristics
- `$RHET_{it}$` = Measures of racial heterogeneity
- `$DENSITY_{it}$` = SMSA population density
- `$GROW_{it}$` = Annualized population growth 
- `$\widehat{OVERLAP}_{it}$` = Predicted jurisdictional overlap
- `$\phi$` = state FE, `$\tau$` = common time effect, `$\varepsilon$` = typical error term

---

## Instruments

Concern that segregation leads to more overlapping governments.

Exploit exogenous variation in local geography to instrument for overlapping governments 
1. Mean slope (degree from horizontal)
2. Miles of river segments (of segments at least 3.5 miles)
Both sourced from the USGS

<br />

`$$\begin{split}
OVERLAP_{it} & =  \beta_{ij} + \beta_2 DEMO_{it} + \beta_3 RHET_{it} + \beta_4 DENSITY_{it} + \beta_5 GROW_{it} \\
& + \beta_6  SLOPE_i + \beta_7  RIVERS_i + \phi_i + \tau_t + \varepsilon_{it}
\end{split}$$`

---

## Descriptive statistics

---

## Descriptive statistics

<table style="width:85%; font-size: 20px; margin-left: auto; margin-right: auto;" class="table">
 <thead>
  <tr>
   <th style="text-align:left;"> Variable </th>
   <th style="text-align:right;"> Mean </th>
   <th style="text-align:right;"> St. Dev </th>
   <th style="text-align:right;"> Min. </th>
   <th style="text-align:right;"> Max. </th>
  </tr>
 </thead>
<tbody>
  <tr grouplength="4"><td colspan="5" style="border-bottom: 1px solid;"><em>Racial heterogeneity measures</em></td></tr>
<tr>
   <td style="text-align:left;padding-left: 2em;" indentlevel="1"> Racial Herfendahl index </td>
   <td style="text-align:right;"> 0.328 </td>
   <td style="text-align:right;"> 0.165 </td>
   <td style="text-align:right;"> 0.022 </td>
   <td style="text-align:right;"> 0.723 </td>
  </tr>
  <tr>
   <td style="text-align:left;padding-left: 2em;" indentlevel="1"> BW difference, percent younger than 15 </td>
   <td style="text-align:right;"> 0.082 </td>
   <td style="text-align:right;"> 0.036 </td>
   <td style="text-align:right;"> 0.000 </td>
   <td style="text-align:right;"> 0.298 </td>
  </tr>
  <tr>
   <td style="text-align:left;padding-left: 2em;" indentlevel="1"> BW difference, percent older than 60 </td>
   <td style="text-align:right;"> 0.088 </td>
   <td style="text-align:right;"> 0.047 </td>
   <td style="text-align:right;"> 0.000 </td>
   <td style="text-align:right;"> 0.394 </td>
  </tr>
  <tr>
   <td style="text-align:left;padding-left: 2em;" indentlevel="1"> BW difference, percent in poverty </td>
   <td style="text-align:right;"> 0.194 </td>
   <td style="text-align:right;"> 0.074 </td>
   <td style="text-align:right;"> 0.003 </td>
   <td style="text-align:right;"> 0.803 </td>
  </tr>
  <tr grouplength="3"><td colspan="5" style="border-bottom: 1px solid;"><em>BW demographic characteristics</em></td></tr>
<tr>
   <td style="text-align:left;padding-left: 2em;" indentlevel="1"> Percent younger than 15 </td>
   <td style="text-align:right;"> 0.210 </td>
   <td style="text-align:right;"> 0.029 </td>
   <td style="text-align:right;"> 0.066 </td>
   <td style="text-align:right;"> 0.341 </td>
  </tr>
  <tr>
   <td style="text-align:left;padding-left: 2em;" indentlevel="1"> Percent older than 60 </td>
   <td style="text-align:right;"> 0.179 </td>
   <td style="text-align:right;"> 0.046 </td>
   <td style="text-align:right;"> 0.048 </td>
   <td style="text-align:right;"> 0.426 </td>
  </tr>
  <tr>
   <td style="text-align:left;padding-left: 2em;" indentlevel="1"> Percent in poverty </td>
   <td style="text-align:right;"> 0.121 </td>
   <td style="text-align:right;"> 0.042 </td>
   <td style="text-align:right;"> 0.040 </td>
   <td style="text-align:right;"> 0.397 </td>
  </tr>
  <tr grouplength="2"><td colspan="5" style="border-bottom: 1px solid;"><em>Other MSA controls</em></td></tr>
<tr>
   <td style="text-align:left;padding-left: 2em;" indentlevel="1"> Population growth rate </td>
   <td style="text-align:right;"> 0.011 </td>
   <td style="text-align:right;"> 0.013 </td>
   <td style="text-align:right;"> -0.131 </td>
   <td style="text-align:right;"> 0.069 </td>
  </tr>
  <tr>
   <td style="text-align:left;padding-left: 2em;" indentlevel="1"> Population density </td>
   <td style="text-align:right;"> 437.473 </td>
   <td style="text-align:right;"> 850.102 </td>
   <td style="text-align:right;"> 11.462 </td>
   <td style="text-align:right;"> 13776.385 </td>
  </tr>
</tbody>
</table>

---

## Findings

<table style="width:85%;border-bottom: 0; font-size: 18px; margin-left: auto; margin-right: auto;" class="table">
 <thead>
  <tr>
   <th style="text-align:left;">  </th>
   <th style="text-align:center;"> Metrowide segregation </th>
   <th style="text-align:center;"> Between city segregation </th>
  </tr>
 </thead>
<tbody>
  <tr grouplength="2"><td colspan="3" style="border-bottom: 1px solid;"><em>Overlapping governments</em></td></tr>
<tr>
   <td style="text-align:left;padding-left: 2em;" indentlevel="1"> Jurisdictional overlap </td>
   <td style="text-align:center;"> 0.357** </td>
   <td style="text-align:center;"> 0.308 </td>
  </tr>
  <tr>
   <td style="text-align:left;padding-left: 2em;" indentlevel="1">  </td>
   <td style="text-align:center;"> 0.109 </td>
   <td style="text-align:center;"> 0.162 </td>
  </tr>
  <tr grouplength="3"><td colspan="3" style="border-bottom: 1px solid;"><em>Model summary</em></td></tr>
<tr>
   <td style="text-align:left;padding-left: 2em;" indentlevel="1"> F-stat. for instrument significance </td>
   <td style="text-align:center;"> 13.840** </td>
   <td style="text-align:center;"> 13.840** </td>
  </tr>
  <tr>
   <td style="text-align:left;padding-left: 2em;" indentlevel="1"> N </td>
   <td style="text-align:center;"> 309 </td>
   <td style="text-align:center;"> 309 </td>
  </tr>
  <tr>
   <td style="text-align:left;padding-left: 2em;" indentlevel="1"> T </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 4 </td>
  </tr>
</tbody>
<tfoot><tr><td style="padding: 0; " colspan="100%">
<span style="font-style: italic;">Note: </span> <sup></sup> Excluded instruments: average slope and number of river miles. Significance levels: ** p&lt;0.01, * p&lt;0.05. All coefficients reported as elasticites at the mean.</td></tr></tfoot>
</table>

---

## Controls

<table style="width:85%; font-size: 14px; margin-left: auto; margin-right: auto;" class="table">
 <thead>
<tr>
<th style="empty-cells: hide;border-bottom:hidden;" colspan="1"></th>
<th style="border-bottom:hidden;padding-bottom:0; padding-left:3px;padding-right:3px;text-align: center; " colspan="2"><div style="border-bottom: 1px solid #ddd; padding-bottom: 5px; ">Metrowide segregation</div></th>
<th style="border-bottom:hidden;padding-bottom:0; padding-left:3px;padding-right:3px;text-align: center; " colspan="2"><div style="border-bottom: 1px solid #ddd; padding-bottom: 5px; ">Between city segregation</div></th>
</tr>
  <tr>
   <th style="text-align:left;">  </th>
   <th style="text-align:center;"> Elasticity </th>
   <th style="text-align:center;"> S.E. </th>
   <th style="text-align:center;"> Elasticity </th>
   <th style="text-align:center;"> S.E. </th>
  </tr>
 </thead>
<tbody>
  <tr grouplength="4"><td colspan="5" style="border-bottom: 1px solid;"><em>Racial heterogeneity measures</em></td></tr>
<tr>
   <td style="text-align:left;padding-left: 2em;" indentlevel="1"> Racial Herfendahl index </td>
   <td style="text-align:center;"> 0.763** </td>
   <td style="text-align:center;"> 0.057 </td>
   <td style="text-align:center;"> 0.760** </td>
   <td style="text-align:center;"> 0.084 </td>
  </tr>
  <tr>
   <td style="text-align:left;padding-left: 2em;" indentlevel="1"> BW difference, percent younger than 15 </td>
   <td style="text-align:center;"> 0.092* </td>
   <td style="text-align:center;"> 0.045 </td>
   <td style="text-align:center;"> 0.071 </td>
   <td style="text-align:center;"> 0.067 </td>
  </tr>
  <tr>
   <td style="text-align:left;padding-left: 2em;" indentlevel="1"> BW difference, percent older than 60 </td>
   <td style="text-align:center;"> -0.174** </td>
   <td style="text-align:center;"> 0.049 </td>
   <td style="text-align:center;"> -0.209** </td>
   <td style="text-align:center;"> 0.073 </td>
  </tr>
  <tr>
   <td style="text-align:left;padding-left: 2em;" indentlevel="1"> BW difference, percent in poverty </td>
   <td style="text-align:center;"> 0.218** </td>
   <td style="text-align:center;"> 0.049 </td>
   <td style="text-align:center;"> 0.157* </td>
   <td style="text-align:center;"> 0.073 </td>
  </tr>
  <tr grouplength="3"><td colspan="5" style="border-bottom: 1px solid;"><em>BW demographic characteristics</em></td></tr>
<tr>
   <td style="text-align:left;padding-left: 2em;" indentlevel="1"> Percent younger than 15 </td>
   <td style="text-align:center;"> 0.013 </td>
   <td style="text-align:center;"> 0.178 </td>
   <td style="text-align:center;"> 0.500 </td>
   <td style="text-align:center;"> 0.265 </td>
  </tr>
  <tr>
   <td style="text-align:left;padding-left: 2em;" indentlevel="1"> Percent older than 60 </td>
   <td style="text-align:center;"> 0.619** </td>
   <td style="text-align:center;"> 0.132 </td>
   <td style="text-align:center;"> 0.906** </td>
   <td style="text-align:center;"> 0.197 </td>
  </tr>
  <tr>
   <td style="text-align:left;padding-left: 2em;" indentlevel="1"> Percent in poverty </td>
   <td style="text-align:center;"> -0.281** </td>
   <td style="text-align:center;"> 0.06 </td>
   <td style="text-align:center;"> -0.450** </td>
   <td style="text-align:center;"> 0.089 </td>
  </tr>
  <tr grouplength="3"><td colspan="5" style="border-bottom: 1px solid;"><em>Other MSA controls</em></td></tr>
<tr>
   <td style="text-align:left;padding-left: 2em;" indentlevel="1"> Population growth rate </td>
   <td style="text-align:center;"> -0.040 </td>
   <td style="text-align:center;"> 0.021 </td>
   <td style="text-align:center;"> -0.051 </td>
   <td style="text-align:center;"> 0.032 </td>
  </tr>
  <tr>
   <td style="text-align:left;padding-left: 2em;" indentlevel="1"> Population density </td>
   <td style="text-align:center;"> 0.032** </td>
   <td style="text-align:center;"> 0.01 </td>
   <td style="text-align:center;"> 0.037* </td>
   <td style="text-align:center;"> 0.015 </td>
  </tr>
  <tr>
   <td style="text-align:left;padding-left: 2em;" indentlevel="1"> State FE </td>
   <td style="text-align:center;"> Yes </td>
   <td style="text-align:center;">  </td>
   <td style="text-align:center;"> Yes </td>
   <td style="text-align:center;">  </td>
  </tr>
  <tr grouplength="3"><td colspan="5" style="border-bottom: 1px solid;"><em>Model summary</em></td></tr>
<tr>
   <td style="text-align:left;padding-left: 2em;" indentlevel="1"> F-stat. for instrument significance </td>
   <td style="text-align:center;"> 13.840** </td>
   <td style="text-align:center;">  </td>
   <td style="text-align:center;"> 13.840** </td>
   <td style="text-align:center;">  </td>
  </tr>
  <tr>
   <td style="text-align:left;padding-left: 2em;" indentlevel="1"> N </td>
   <td style="text-align:center;"> 309 </td>
   <td style="text-align:center;">  </td>
   <td style="text-align:center;"> 309 </td>
   <td style="text-align:center;">  </td>
  </tr>
  <tr>
   <td style="text-align:left;padding-left: 2em;" indentlevel="1"> T </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;">  </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;">  </td>
  </tr>
</tbody>
</table>

---

## Discussion

- Increasing numbers of overlapping local governments leads to an increase in Black-white racial segregation 
  - A ten percent increase in overlap → 3.6 percent increase in metropolitan-wide segregation 
  - The results appear driven by within-city changes in segregation (between city measures show no association)
- While municipalities undoubtedly drive some portion of racial segregation through restrictive land use regulations, overlapping governments can accomplish similar results

---
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