Question

outline two conditions upon which Difference-in-Difference (DHD) technique is an appropriate method to obtain an appropriate counterfactual to estimate a casual effect.

Answer 1

DID is a quasi-experimental design that makes use of longitudinal data from treatment and control groups to obtain an appropriate counterfactual to estimate a causal effect. DID is typically used to estimate the effect of a specific intervention or treatment (such as a passage of the law, enactment of policy, or large-scale program implementation) by comparing the changes in outcomes over time between a population that is enrolled in a program (the intervention group) and a population that is not (the control group).

DID is used in observational settings where exchangeability cannot be assumed between the treatment and control groups. DID relies on a less strict exchangeability assumption, i.e., in the absence of treatment, the unobserved differences between treatment and control groups are the same over time. Hence, Difference-in-difference is a useful technique to use when randomization on the individual level is not possible. DID requires data from pre-/post-intervention, such as cohort or panel data (individual-level data over time) or repeated cross-sectional data (individual or group level). The approach removes biases in post-intervention period comparisons between the treatment and control group that could be the result of permanent differences between those groups, as well as biases from comparisons over time in the treatment group that could be the result of trends due to other causes of the outcome.

Causal Effects (Ya=1 – Ya=0)
DID usually is used to estimate the treatment effect on the treated (causal effect in the exposed), although with stronger assumptions the technique can be used to estimate the Average Treatment Effect (ATE) or the causal effect in the population. Please refer to Lechner 2011 article for more details.

ASSUMPTIONS

In order to estimate any causal effect, three assumptions must hold: exchangeability, positivity, and Stable Unit Treatment Value Assumption (SUTVA)1
. DID estimation also requires that:

• Intervention unrelated to the outcome at baseline (allocation of the intervention was not determined by outcome)

• Treatment/intervention and control groups have Parallel Trends in the outcome (see below for details)

• Composition of intervention and comparison groups is stable for repeated cross-sectional design (part of SUTVA)

• No spillover effects (part of SUTVA)

Parallel Trend Assumption
The parallel trend assumption is the most critical of the above four assumptions to ensure the internal validity of DID models and is the hardest to fulfill. It requires that in the absence of treatment, the difference between the ‘treatment’ and ‘control’ group is constant over time. Although there is no statistical test for this assumption, visual inspection is useful when you have observations over many time points. It has also been proposed that the smaller the time period tested, the more likely the assumption is to hold. Violation of the parallel trend assumptions will lead to a biased estimation of the causal effect.

Meeting the Parallel Trend Assumption 2	Violation of the Parallel Trend Assumption 3

Regression Model
DID is usually implemented as an interaction term between time and treatment group dummy variables in a regression model.
Y= β0 + β1*[Time] + β2*[Intervention] + β3*[Time*Intervention] + β4*[Covariates]+ε

Strengths and Limitations
Strengths

• Intuitive interpretation

• Can obtain causal effect using observational data if assumptions are met

• Can use either individual and group level data

• Comparison groups can start at different levels of the outcome. (DID focuses on changerather than absolute levels)

• Accounts for change/change due to factors other than intervention

Limitations

• Requires baseline data & a non-intervention group

• Cannnot use if intervention allocation determined by baseline outcome

• Cannot use if comparison groups have different outcome trend (Abadie 2005 has proposed solution)

• Cannot use if composition of groups pre/post change are not stable