When do covariates rescue a difference-in-differences?
A job-training program raised earnings by a known $1,794 — we know because it was evaluated with a randomized trial. Throw the experimental control away, swap in a survey of ordinary Americans, and a naive difference-in-differences returns $3,621: roughly twice the truth. This is the LaLonde test. The question is whether covariates can fix it — and whether where you put them matters.
Additive controls. Time-invariant, so two-way fixed effects sweep them out. Inert.
Heterogeneous treatment effects. Relaxes constant effects but never touches the trend. Inert.
Bends the control group's counterfactual trend — the reason the naive estimate is wrong. Corrected.
The whole story is that only the last placement addresses the problem. Because the survey controls are wildly different from the trainees, and groups with different characteristics are on different earnings trajectories, that imbalance mechanically breaks parallel trends — and only covariates in the trend can repair it. Open the Spec Explorer to watch the estimate move.
Reproduces Scott Cunningham's “Covariates, diff in diff and LaLonde test.” Estimand: the ATT. Data: Dehejia-Wahba NSW + CPS controls.
Climb the ladder: where does the covariate enter?
Step through the specifications in order. The estimate is flat at $3,621 while covariates sit in the level or the treatment effect, then snaps toward the benchmark the instant they enter the trend.
The raw 2×2 difference-in-differences, with no covariates at all. The number to beat.
Why the naive estimate is wrong
The control group's raw earnings path is the crux. The CPS controls sit far above the trainees and drift on a different slope; the randomized controls track the trainees. A DiD that uses the CPS as-is assumes the trainees would have followed that high, flat path — which is not credible.
Mean real earnings by group, 1974–1978. Imbalance in levels becomes bias only because the groups are also on different trends — exactly the gap that covariate-by-time interactions close.