19 D4. Causal Inference — Overview
19.1 About
A central challenge in empirical economics is distinguishing correlation from causation. We observe associations in data, but the causal interpretation requires careful design.
The fundamental problem of causal inference
For each unit \(i\), define potential outcomes \((Y_i(1), Y_i(0))\) — the outcome under treatment and control, respectively. The causal effect for unit \(i\) is:
\[\tau_i = Y_i(1) - Y_i(0)\]
We only observe one of the two potential outcomes. This is the fundamental problem of causal inference (Holland, 1986). Identification requires assumptions about the relationship between treatment assignment and potential outcomes.
Randomized controlled trials (RCTs)
When treatment \(D_i\) is randomly assigned, \(D_i \perp (Y_i(0),Y_i(1))\), so: \[E[Y_i(1)] - E[Y_i(0)] = E[Y_i \mid D_i=1] - E[Y_i \mid D_i=0]\]
The difference in means is the Average Treatment Effect (ATE). RCTs are the gold standard but are often infeasible (cost, ethics, scale).
19.2 Observational Strategies
When randomization is not available, economists use quasi-experimental methods:
| Method | Identification assumption |
|---|---|
| DiD (Difference-in-Differences) | Parallel trends in the absence of treatment |
| RDD (Regression Discontinuity Design) | Continuity of potential outcomes at the threshold |
| IV (Instrumental Variables) | Instrument relevance + exclusion restriction |
| Matching / Selection on observables | Conditional independence: \(D_i \perp Y_i(0), Y_i(1) \mid X_i\) |
This block covers DiD and RDD. IV is covered in Bloque C.
19.3 Sections
- D5. Difference-in-Differences — two-way FE, parallel trends, event study, staggered DiD.
- D6. Regression Discontinuity Design — sharp vs. fuzzy RDD, local linear regression, bandwidth selection.
19.4 References
Angrist, J. D. and Pischke, J.-S. (2009). Mostly Harmless Econometrics. Princeton University Press.
Imbens, G. W. and Rubin, D. B. (2015). Causal Inference for Statistics, Social, and Biomedical Sciences. Cambridge University Press.