DiD and FD

What does the coefficient on the interaction term (Treatment × Time) capture in a DiD model?

• Average difference in outcomes between groups at any time

• Time trend common to all units

• Average Treatment Effect on the Treated (ATT)

• Difference between treatment and control groups before the event

Why would a model with only the time dummy (e.g. y = β₀ + β₁·y2007) be insufficient to identify the treatment effect?

• It cannot account for any change in the outcome variable

• It cannot separate the treatment effect from general time trends

• It always leads to perfect multicollinearity

• It includes too many control variables

Why is it problematic to estimate a treatment effect using only treated units before and after the program (no control group)?

• It's mathematically incorrect

• The variance of the estimator is zero

• It leads to overfitting

• Unobserved time trends could bias the estimated effect

In the first-difference model Δy = β₁Δx + Δu, what happens to time-invariant individual heterogeneity αᵢ?

• It becomes part of the error term

• It is captured by Δx

• It is differenced out and disappears

Why can’t you include “age” in a first-difference model across consecutive years?

• Age is not a relevant variable

• Its difference is always 1, which creates perfect multicollinearity with the constant

• It has too many missing values

• Age is already accounted for in the error term

Why can the effect of place of birth not be estimated in a first-difference model?

• It is not linearly related to the outcome

• It changes too frequently

• It is time-invariant and disappears when differencing

• It is endogenous

What is a key assumption for the validity of the DiD approach?

• Random assignment of treatment

• Parallel trends between treatment and control groups

• Equal sample sizes in each group

Why can First Differences estimation not eliminate bias from time-varying unobserved heterogeneity?

• Because it assumes time-invariant unobservables are zero

• Because it differences out both observed and unobserved variables

• Because differencing only removes unobserved factors that do not change over time