Randomly Assigned First Differences?

Cl\'ement de Chaisemartin and Ziteng Lei

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Abstract: We consider treatment-effect estimation using a first-difference regression of an outcome evolution $\Delta Y$ on a treatment evolution $\Delta D$. Under a causal model in levels, the residual of the first-difference regression is a function of the period-one treatment $D_{1}$. Then, researchers should test if $\Delta D$ and $D_{1}$ are correlated: if they are, the first-difference regression may suffer from an omitted variable bias. To solve it, researchers may control for $E(\Delta D|D_{1})$. We apply these results to regressions of US industries' employment evolutions on the evolution of their Chinese imports, estimated on the data of \cite{acemoglu2016import}. $\Delta D$ and $D_{1}$ are strongly correlated. Controlling for $E(\Delta D|D_{1})$ halves the estimated effect of Chinese imports.

Date: 2024-11, Revised 2025-01
New Economics Papers: this item is included in nep-ecm
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