CBS TWFE decomposition weights

Pick a decomposition from Table 1 of Callaway, Goodman-Bacon & Sant'Anna (v4). Dose distribution: 155 Chinese industries a la Lu & Yu (2015) — ~30% at D=0, right-skewed positive doses up to 0.60.

Level weight: $w^{\text{lev}}(l) = \dfrac{(l - E[D])\cdot f_D(l)}{\text{Var}(D)}$

Six ingredients

$E[D]$

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$\text{Var}(D)$

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$P(D=0)$

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$d_L$

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$d_U$

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$f_D(l)$

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Plug in the numbers at the chosen l

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Coming soon

$w^{s}(l) = \dfrac{l \cdot (l - E[D]) \cdot f_D(l)}{\text{Var}(D)}$

Integrates to 1 but still has negative weights below the mean.

Coming soon

$w^{\text{acrt}}(l) = \dfrac{(E[D \mid D \ge l] - E[D])\cdot P(D \ge l)}{\text{Var}(D)}$

Non-negative and integrates to 1 — but not the dose density.

Coming soon

$w^{2\times 2}(l, h) = \dfrac{(h - l)^{2} \cdot f_D(h) \cdot f_D(l)}{\text{Var}(D)}, \quad h > l$

Heatmap over the triangular region.