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.
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.