A researcher compares employed-at-follow-up rates between job training program participants and non-participants, and finds participants have higher employment. Why can't they conclude the program caused the difference?
AEmployment is too volatile to measure accurately at a single point in time
BThe groups may have differed in employment motivation or qualifications before the program — selection bias means the comparison confounds the treatment effect with pre-existing differences
CThe sample size is probably too small to detect a real causal effect
DThey need regression adjustment for age and education before any comparison is valid
People who seek out job training may be more motivated or better-connected than those who don't — the groups differ for reasons unrelated to the program itself. This is selection bias: the naive comparison captures both the treatment effect (if any) and these pre-existing differences. DiD solves this by using the control group's over-time change to estimate what the treatment group's trajectory would have looked like absent the program, removing the confound.
Question 2 Multiple Choice
In a DiD study: the treatment group averages $80 pre-treatment and $90 post-treatment. The control group averages $60 pre-treatment and $65 post-treatment. What is the DiD estimate of the treatment effect?
A$10 — the treated group's pre-to-post change
B$25 — the post-treatment difference between the groups
C$5 — the treated group's change ($10) minus the control group's change ($5)
D$20 — the pre-treatment difference between the groups
DiD = (Ȳ_treated,post − Ȳ_treated,pre) − (Ȳ_control,post − Ȳ_control,pre) = (90 − 80) − (65 − 60) = 10 − 5 = $5. The control group's $5 change represents what would have happened to the treatment group over the same period without the treatment (under parallel trends). Subtracting it removes the common time trend, leaving only the treatment effect. The $10 and $25 figures are both biased — they fail to remove the underlying time trend.
Question 3 True / False
For a DiD design to be valid, the treatment and control groups should have similar outcome levels before the treatment period.
TTrue
FFalse
Answer: False
This is the most important misconception about the parallel trends assumption. Parallel trends requires only that the two groups would have moved in parallel over time absent treatment — they can have very different absolute levels. A high-unemployment state and a low-unemployment state can satisfy parallel trends as long as their trends (changes over time) are similar. Differences in levels are removed by the first differencing step; they don't threaten the design.
Question 4 True / False
The DiD estimator removes the bias from any time-constant difference between the treatment and control groups, because taking pre-to-post changes within each group eliminates stable between-group differences.
TTrue
FFalse
Answer: True
This is the core identifying power of DiD. Any stable difference between groups — whether from selection, geography, demographics, or other confounders — is differenced out when you compute the pre-to-post change within each group. What remains after the double-difference is only the portion of the treated group's change that exceeds the control group's change over the same period, which under parallel trends reflects the treatment effect.
Question 5 Short Answer
What is the parallel trends assumption in DiD, and why can it not be directly tested at the exact time of treatment?
Think about your answer, then reveal below.
Model answer: Parallel trends assumes that absent treatment, the treatment and control groups would have followed the same trajectory over the treatment period — changed by the same amount. It cannot be directly tested at the treatment time because we never observe what the treatment group would have done without treatment — that is the fundamental counterfactual problem. We can support it by verifying parallel pre-treatment trends and arguing by analogy that this would have continued, but we cannot prove it for the treatment period itself.
This untestability is not a defect unique to DiD — it is the fundamental problem of causal inference. All causal identification strategies rest on untestable assumptions about counterfactuals. DiD's strength is that parallel pre-trends provide visible, testable support for the assumption, making violations detectable if the groups were already diverging before treatment.