Policy evaluation with a treated and control group, parallel trends and the 2×2 table.
Warming up the engine…
Difference-in-differences: compare treated and control groups before and after a policy; the double difference removes both group and time confounds, if trends were parallel.
β_DiD = (ȳ_T,post − ȳ_T,pre) − (ȳ_C,post − ȳ_C,pre)
The control group supplies the counterfactual: what would have happened to the treated anyway. Everything hangs on parallel trends, plot the pre-period paths, and if they already diverged, the design is dead on arrival.
Draw the 2×2 table and SHOW the subtraction; then name the parallel-trends check as your validity argument.
Now prove you have it
Move the curve to where you think it lands, and get told exactly which part you got right.
Real-world scenarios on this model
Also in Econometrics
Equilibrium at t 5.0, Y 40.
Equilibrium: t* = 5.0, Y* = 40.0
Current equations
A policy hits one group and not another. Watch both lines before the policy date: they move in parallel. After the date, the treated line lifts above where its old trend was heading. That lift is the policy's effect, measured as a difference of differences.
Source: Wooldridge, ch. 13; Card & Krueger (1994)