moderndid.compute_identified_set_rmb#

moderndid.compute_identified_set_rmb(m_bar, true_beta, l_vec, num_pre_periods, num_post_periods, bias_direction='positive')[source]#

Compute identified set for \(\Delta^{RMB}(\bar{M})\).

Computes the identified set for \(l'\tau_{post}\) under the restriction \(\delta \in \Delta^{RM}(\bar{M}) \cap \Delta^B\).

The identified set is the union of identified sets for each component polyhedron, as stated in (7) of [2]

\[\mathcal{S}(\beta, \Delta^{RMB}(\bar{M})) = \bigcup_{s<0, \text{sign} \in \{+,-\}} \mathcal{S}(\beta, \Delta^{RM}_{s, \text{sign}}(\bar{M}) \cap \Delta^B).\]

For each component, the bounds are determined by solving the linear programs from Lemma 2.1 of [2].

Parameters:
m_barfloat

Relative magnitude parameter \(\bar{M}\).

true_betanumpy.ndarray

True coefficient values (pre and post periods).

l_vecnumpy.ndarray

Vector defining parameter of interest.

num_pre_periodsint

Number of pre-treatment periods.

num_post_periodsint

Number of post-treatment periods.

bias_direction{‘positive’, ‘negative’}, default=’positive’

Direction of bias sign restriction.

Returns:
DeltaRMBResult

Lower and upper bounds of the identified set.

References

[1]

Andrews, I., Roth, J., & Pakes, A. (2021). Inference for linear conditional moment inequalities. Review of Economic Studies.

[2] (1,2)

Rambachan, A., & Roth, J. (2023). A more credible approach to parallel trends. Review of Economic Studies, 90(5), 2555-2591.