Causal Inference 3
Observational Data
Jeremy Springman
University of Pennsylvania
Global Development: Intermediate Topics in Politics, Policy, and Data
PSCI 3200 - Spring 2024
Logistics
Assignments
- Today
- DSS Ch 5
- Create a git repo for this class (psci3200_yourname)
- Monday
- Migration readings (will post before Monday)
- Git repo workshop (semi-optional)
Agenda
- Review Linear Regression
- Causal Inference with Observational Data (pt. 1)
- Workshop
- Causal Inference with Observational Data (pt. 2)
Linear Regression
Linear Regression Model
\[ Y_i = \alpha + \beta X_i + \epsilon_i \]
Linear Regression Model
Estimating model parameters
\[ \hat{Y_i} = \hat{\alpha} + \hat{\beta} X_i \] Coefficient \[ \hat{\beta} = \Delta{\hat{Y}} / \Delta{X} \]
Minimizing the Residuals
What are residuals
\[ \hat{\epsilon_i} = Y_i - \hat{Y_i} \]
How do we minimize them?
\[ SSR = \sum_{i}^{N} \hat{\epsilon}_i^2 \]
Casaul Inference 3 (pt. 1)
Causality without Randomization
- You must control for…
- everything (observed and unobserved) that affects both the treatment variable and the outcome variable
- You must not control for…
- anything that is affected by both the treatment variable and the outcome variable
- You need to think carefully before controlling for…
- anything that is affected by the treatment variable that also affects the outcome variable
Multiple Regression
\[ Y_i = \alpha + \beta_1 X_{i1} + \beta_2 X_{i2} + \epsilon_i \]
- How does our interpretation of \(\alpha\) change?
- How does our interpretation of \(\beta_1\) change?
Threats to Inference
- Confounders
- Colliders
- Mechanisms
- Reverse Causality
Workshop
Casaul Inference 3 (pt. 2)
Identification strategy
In the real world, there are always threats to inference that we can’t measure/observe or understand well enough to adjust for
- A research design that allows us to isolate a causal effect from observational data
- Approximates an experiment by ensuring that the treatment and control group are similar at baseline
- These strategies rely on assumptions that we can attempt to validate
Holy Trinity of Causal Inference
- Difference-in-Differences
- Regression Discontinuity
- Instrumental Variables
Validity
- Internal validity
- External validity
- What are the trade-offs between experiments and observational studies?
- Experiments have more internal validity
- But… they often have synthetic treatments, convenience samples
- Where are these studies used in the real-world?
Adjusting on Observables
- Matching
- Weighting
- Synthetic Control (very fancy weighting)
jrspringman.github.io/psci3200-globaldev/