moderndid.compute_identified_set_sdrmb

moderndid.compute_identified_set_sdrmb(m_bar, true_beta, l_vec, num_pre_periods, num_post_periods, bias_direction='positive')

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

Computes the identified set for \(l'\tau_{post}\) under the restriction that the underlying trend delta lies in \(\Delta^{SDRMB}(\bar{M})\).

The identified set under \(\Delta^{SDRMB}(\bar{M})\) represents the values of \(\theta = l'\tau_{post}\) consistent with the observed pre-treatment coefficients \(\beta_{pre} = \delta_{pre}\), the combined smoothness and relative magnitude constraints, and a sign restriction on the post-treatment bias, as described in Section 2.4.4 of [1].

The set is constructed by taking the union of identified sets for each sub-polyhedron, each corresponding to a specific pre-treatment period s and sign for the maximum second difference, intersected with the bias sign restriction.

Parameters:

m_barfloat

Relative magnitude parameter. Second differences in post-treatment periods can be at most \(\bar{M}\) times the maximum absolute second difference in pre-treatment periods.

true_betanumpy.ndarray

True coefficient values (pre and post periods).

l_vecnumpy.ndarray

Vector defining parameter of interest \(\theta = l'\tau_{post}\).

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:

DeltaSDRMBResult

Lower and upper bounds of the identified set.

Notes

The identified set is computed by solving linear programs for each choice of period \(s\) and sign (positive/negative maximum), then taking the union of all resulting intervals, intersected with the sign restriction.

References

[1]

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