Causal inference
Methods for estimating causal effects from observational data using quasi-experimental variation — discontinuities, differential timing, excluded instruments, or covariate balance — without structural assumptions.
Observational data conflates treatment selection with treatment effects. Units that receive treatment differ systematically from those that don't — any naive comparison is confounded.
The goal is to find variation in treatment that is as-good-as-random: a policy cutoff, a natural experiment, an instrument. Each method isolates one such source of clean variation.
Choosing a method means choosing an identifying assumption. That assumption must be plausible, testable where possible, and clearly stated.
library(fixest)
# Two-way fixed effects DiD
feols(
insured ~ i(year, treated, ref = 2013) | state + year,
data = acs_panel,
cluster = ~state
) |> iplot(
main = "Effect of Medicaid expansion",
xlab = "Year relative to expansion"
)Difference-in-differences
Compares changes over time between treated and untreated groups. The workhorse of policy evaluation — valid even with selection into treatment, so long as trends would have matched.
Event study
Plots treatment effects at each period relative to the event. Tests pre-trends visually and estimates dynamic effects — essential for any DiD specification.
Instrumental variables
Exploits a variable that shifts treatment but has no direct path to the outcome. Recovers a LATE for compliers. Requires careful instrument selection and weak-instrument diagnostics.
Regression discontinuity
Identifies causal effects near an arbitrary cutoff in an assignment rule. Sharp designs give clean identification; fuzzy designs require an IV argument. Bandwidth selection is critical.
Matching & IPW
Constructs a valid comparison group by balancing observed covariates through matching or reweighting. Assumes no unobserved confounding — every common cause of T and Y must be observed.
Synthetic control
Constructs a weighted combination of control units that matches the pre-treatment trajectory of the treated unit. Best suited for comparative case studies with a single treated aggregate.