Compute diff-in-diff and pretrend flag

You are given individual-level observational data for an experiment-like setting with:

• period[i] ∈ {0,1}: 0 = pre period, 1 = post period
• treatment[i] ∈ {0,1}: 1 = treated group, 0 = control group
• outcome[i] ∈ ℝ: numeric outcome

All three arrays have the same length N, and row i corresponds to one observation.

Tasks

1. Compute the Difference-in-Differences (DiD) estimate of the treatment effect:

$\text{DiD} = (\bar{Y}_{T,post} - \bar{Y}_{T,pre}) - (\bar{Y}_{C,post} - \bar{Y}_{C,pre})$

where the bars denote sample means over the corresponding subsets.

2. Compute a pretrend flag using the following simplified rule:

• Let $d_{pre} = |\bar{Y}_{T,pre} - \bar{Y}_{C,pre}|$ .
• Given a real number threshold , return pretrend=True if $d_{pre} > \text{threshold}$ , else False .

Output

Return:

• did_estimate (float)
• pretrend (boolean)

Assumptions / edge cases

• If any of the required cells (T/C × pre/post) has zero observations, specify and implement a reasonable behavior (e.g., raise an error or return NaN).