moderndid.didinter.variance.compute_joint_test#

moderndid.didinter.variance.compute_joint_test(estimates, vcov)[source]#

Compute joint Wald test that all estimates are zero.

Computes a chi-squared test statistic for the null hypothesis \(H_0: \delta_1 = \delta_2 = \cdots = \delta_L = 0\). For placebo effects, this tests the parallel trends assumption by checking whether pre-treatment outcome trends differ between switchers and non-switchers. The test statistic is

\[W = \hat{\boldsymbol{\delta}}' \widehat{\mathbf{V}}^{-1} \hat{\boldsymbol{\delta}} \sim \chi^2_L\]

where \(\hat{\boldsymbol{\delta}}\) is the vector of estimates and \(\widehat{\mathbf{V}}\) is the variance-covariance matrix.

Parameters:

estimatesnumpy.ndarray: Point estimates \(\hat{\boldsymbol{\delta}}\).
vcovnumpy.ndarray: Variance-covariance matrix \(\widehat{\mathbf{V}}\).

Returns:

dict or None: Dictionary with chi2_stat, df, p_value, and warnings list, or None if computation fails.

References

[1]

de Chaisemartin, C., & D’Haultfoeuille, X. (2024). Difference-in- Differences Estimators of Intertemporal Treatment Effects. Review of Economics and Statistics, 106(6), 1723-1736.