Political Science and Spatial Analysis

• Combining the methods we have learned helps you answer new research questions:
  1. Access/Build a spatial dataset
  2. Conduct spatial operations to combine data
  3. Measure spatial relationships

Political Science and Spatial Analysis

1. Describing spatial location/shape
   • Centroids, Compactness
2. Identifying Clustering
   • Moran’s I, LISA
3. Correlating Spatial Relationships
   • Bivariate Moran’s I, Spatial regression
4. The Effects of Borders
   • Geographic Regression Discontinuity

Gerrymandering

• Geographers are in high demand in Washington DC
  • Politicians try to “pick their electorates”
  • Changing the shape of district boundaries to maximize their chance of re-election
  • Taking advantage of the fact that most votes are ‘wasted’
• “Packing” and “Cracking”
  • Packing your opponents into one district: They only get one seat
  • Cracking your opponents to divide them into multiple districts: No chance of any seats

Gerrymandering

• Easier when politicians control the redistricting process
  • When partisan voters are easily identified by race (a census variable)
  • When voters are clustered: They pack and crack themselves, eg. black voters in the USA (Chen and Rodden 2010)
  • And because there is no ‘correct’ district shape: All maps have partisan effects

Gerrymandering

Gerrymandering

Gerrymandering

Gerrymandering

Gerrymandering

• Measuring Gerymandering
  • State constitutions: “Districts shall be compact…”
  • Efficiently taking up space: the most compact shape is a circle
  • More than 30 measures of compactness!

Gerrymandering

• One compactness test: Polsby-Popper
  • 0 = Low compactness
  • 1 = High compactness (a circle)

\[PP = \frac{4 \pi Area}{Perimeter^2}\]

Gerrymandering

Gerrymandering

• Gerrymandering was becoming less frequent, but got worse since the 1970s

Gerrymandering

• The Efficiency Gap is another (non-spatial) test
  • How many votes did each party waste?
  • Sum each party’s votes in losing districts plus votes above 50% in winning districts
  • Find the difference between parties

• We can also create lots of random maps and measure bias
  • Then compare: How extreme is reality?

Spatial Correlations

• Moran’s I helped us measure the clustering of a variable with itself
  • If income is high in unit \(i\), is income also high in the neighbours of \(i\)?
• But political science questions are often about the relationship between variables
  • If income is high in unit \(i\), is crime also high in the neighbours of \(i\)?

Spatial Correlations

• Univariate Moran’s I

Spatial Correlations

• Bivariate Moran’s I

Spatial Correlations

• Spatial econometrics is often the ‘right’ way to deal with these questions
  • A model of the relationship, not just a descriptive statistic
  • Requires more assumptions
  • But allows for control variables

• Normal regression is no good
  • Assumes no spatial autocorrelation
  • We need to model the spatial autocorrelation so it doesn’t affect our standard errors

Border Effects

• How much do spatial patterns change at a border?
  • How can we measure this statistically?
• A Geographic Regression Discontinuity Design (GRD)
  • People who live on one side of a border are usually very similar to those on the other side
  • On income, race, culture, history etc.
  • They are just governed by different people/policies
  • We can use this to compare and make causal claims

Border Effects

• For example:
  • The effect of the Habsburg Empire on voting today
  • The effect of the Peruvian ‘Mita’ on education
  • The effect of media markets on political attitudes

Border Effects

• Do political adverts change voter turnout?

Border Effects

• Nightlights on the Ukraine-Romania (Pinkovskiy 2013)

Border Effects

• Borders within Switzerland divide language speakers:

Border Effects

• Bihar-Jharkhand Border and Trust in the Civil Service:

Border Effects

• Regression estimate:

\[y_i = \alpha + \beta \text{Border}_i + \gamma \text{Distance to Border}_i + \epsilon_i\]

• We care about the direction and significance of \(\beta\)
  • The effect of the border after controlling for gradual changes across space

Border Effects

• Alternative Regression estimate:
  • x=longitude, y=latitude

\[y_i = \alpha + \beta Border_i + f(x + y + x^2 + y^2 + x^3 + y^3 + x^4 + y^4 + \\ x * y + x^2 * y^2 + x^3 * y^3 + x * y^2 + x * y^3 + x^2 * y + x^3 * y)) + \epsilon_i\]

• We care about the direction and significance of \(\beta\)
  • The effect of the border after controlling for gradual changes across space

Border Effects

• But remember to ask: why is the border located there?
  • Are people actually the same either side of the border? (Balance test)
  • And can’t people migrate?

Summary

1. Spatial analysis is about ‘nearer’ things being more ‘related’
2. Use consistent, appropriate coordinate reference systems!
3. Spatial operations allow you to create new variables and measures
4. Spatial autocorrelation as a threat vs. an opportunity
5. Scale affects our results (eg. MAUP), so try and analyze at lets of scales
6. Maps mislead; understand your data!