Interactive modelEconometricsadvanced

Difference-in-Differences

Policy evaluation with a treated and control group, parallel trends and the 2×2 table.

Equilibrium: t* = 5.0, Y* = 40.0

Current equations

Treated group: Y = 30 + 2·tCounterfactual (parallel trend): Y = 30 + 2·tControl group: Y = 20 + 2·tPolicy starts: t = 5

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)

Shift the curves

Treatment effect of the policy0

The causal effect: how far the treated group lifts above its own counterfactual trend.

The Difference-in-Differences model, in writing

Definition

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 intuition

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.

Exam tip

Draw the 2×2 table and SHOW the subtraction; then name the parallel-trends check as your validity argument.

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