Final Project Essentials 1

Index Measures and Interaction Terms

Author
Affiliation

Jeremy Springman

University of Pennsylvania

Logistics

Assignments

  • Today
    • Final Project Assignment 1: Research question and data source
    • Check your submission (self-contained)
  • Thursday (3/14)
    • Readings

Agenda


  1. Final Project Review
  2. Workshop on Final Project Essentials

Final Project Review

Research Question

Does moving to a new city reduce the political engagement of young people?

  • I hypothesize that moving to a new city will reduce young people’s likelihood of engaging in political or civic action
    • Youth have low levels of political engagement, often driven by lack of information and experience
    • Youth that move have less information and experience with engagement in their new city
    • Youth that move probably have fewer social ties, and ties are important for facilitating engagement

Research Design

  • Design: Estimate the relationship between whether or not an individual moved to a new city to attend university and their level of political engagement
  • Assumption: Individuals that moved to a new city had similar propensities to participate to those that did not, conditional on observable covariates
  • Diagnosis: Unrealistic!
  • Plan: Build confidence by ruling-out potential differences in baseline propensity to participate among moving and non-moving students

Researh Context


  • Students at Addis Ababa University (AAU)
    • Youth frequently move to a new city in order to obtain education
    • AAU is Ethiopia’s top university, and students from around the country move to study there
    • Universities are important sites of political socialization

Building Confidence

Observable implications

  • Identify specific types of participation that are more and less likely to be affected by whether at student moves
    • Some forms of participation rely on social ties or information about the environment, while others do not
  • Account for the length of time since respondents moved to their new city
    • As students become more embedded, the gap between moving and non-moving students should become smaller

Building Confidence

Conditioning

  • Students that move from one urban place to another urban place
    • Students that move from one city to another city will be less different (in their propensity to participate) than those moving from rural to urban
  • Students with similar socio-economic status (SES)
    • Students with similar SES will be less different (in their propensity to participate) than those with similar SES

Building Confidence


Placebo tests

  • Moving may affect feelings about your individual efficacy, but not the efficacy of youth in general
  • Moving may affect your participation recent engagement, but not an opportunity to engage that was provided within the survey

Data and Variables

Data

  • Representative survey of 825 AAU students
  • 2 waves (May-June, October-November of 2022)

Variables

  • Outcome: survey questions measuring political participation
  • Treatment: whether student is originally from Addis Ababa
  • Building confidence: feelings of political efficacy, number of years since move, urban or rural origin, SES, etc.

Final Project Essentials

Creating Index Measures

When to create an index measure

  • When you have many ways of measuring a single concept
    • This is true for outcome measures, treatment measures, and covariates

Benefits of index measures

  • Simplifies analysis (fewer graphs, tables, etc.)
  • Reduces number of hypotheses being tested

Additive Scale

What is an additive scale?

  • Simple sum across columns (index = column_1 + column_2)

When to use an additive scale

  • When variables are measured on a common scale
  • When you are interested in a cumulative amount of something
    • Number of times someone engaged in a specific behavior
    • Amount of money from several different sources

Additive Scale


Benefits of additive scales

  • Interpretability: number on the original scale
  • Simplicity: Just plain addition

Averaged Z-Scores

What is a z-score?

  • \(Z = (X - \mu) / \sigma\)
  • Standardized: Mean of 0 and standard deviation of 1

When to use averaged z-scores

  • When variables are measured on different scales
  • When variables cannot be summed

Averaged Z-Scores


Benefits of averaged z-scores

  • Interpretability: Standard deviations from the mean
  • Outlier detection: abs(3)

Fancier index techniques


  • Principal Component Analysis
  • Factor Analysis
  • Inverse Covariance Weighting

Interaction Terms

What is an interaction term?

  • Simple linear models assume that the effect of predictors is independent of other factors
  • Interaction terms allow us to estimate the difference in the slope of a predictor across unit characteristics

\[ Y_i = \alpha + \beta_1 X_{i1} + \beta_2 X_{i2} + \beta_3 X_{i1}*X_{i2} + \epsilon_i \]

Interaction Terms

What are interaction terms used for?

  • Heterogeneous effects
  • Difference-in-differences

Example: Continuous outcome with two binary predictors

  • \(\alpha\): Intercept when \(X_{i1}\) and \(X_{i2}\) are 0
  • \(\beta_1\) Slope when \(X_{i2} = 0\)
  • \(\beta_2\) Difference in \(\alpha\) between \(X_{i2}=0\) and \(X_{i2}=1\)
  • \(\beta_3\) Difference in \(\beta_1\) between \(X_{i2}=0\) and \(X_{i2}=1\)