Difference-in-Differences

Background

Difference-in-Differences estimates a causal treatment effect when full randomisation isn't possible: take the change in the treatment group over time and subtract the change in the control group over the same time. Group-level baselines cancel; what remains is the treatment effect under the parallel-trends assumption.

Problem statement

Implement did_estimate(y_treat_pre, y_treat_post, y_ctrl_pre, y_ctrl_post):

$$\text{DiD} \;=\; (\bar Y^T_{\text{post}} - \bar Y^T_{\text{pre}}) \;-\; (\bar Y^C_{\text{post}} - \bar Y^C_{\text{pre}})$$

Return a single float.

Input

• y_treat_pre — array-like, treatment-group outcomes before the intervention.
• y_treat_post — array-like, treatment-group outcomes after.
• y_ctrl_pre — array-like, control-group outcomes before.
• y_ctrl_post — array-like, control-group outcomes after.

Output

Returns a Python float.

Examples

Example 1 — both groups change identically → zero treatment effect

Input:  treatment: 1→2; control: 5→6
Output: 0.0

Example 2 — treatment changes more than control → positive DiD

Input:  treatment: 0→3; control: 0→1
Output: 2.0

Example 3 — returns Python float

Input:  any valid arrays
Output: isinstance(result, float)

Constraints

• Each input is a non-empty array-like; the function uses the mean over each group/period.
• Returns a Python float.

Notes

• Parallel-trends assumption. DiD assumes control and treatment would have followed parallel trajectories absent the intervention. Visual inspection of pre-period trends is the standard sanity check.
• Two-way fixed effects. The regression equivalent is Y ~ treated + post + treated:post; the treated:post interaction's coefficient equals DiD. Use that form when you need standard errors and covariates.