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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.03208 |
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| _version_ | 1866909673603465216 |
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| author | Argañaraz, Facundo de Chaisemartin, Clément Lei, Ziteng |
| author_facet | Argañaraz, Facundo de Chaisemartin, Clément Lei, Ziteng |
| contents | We consider treatment-effect estimation using a first-difference regression of an outcome evolution $ΔY$ on a treatment evolution $ΔD$. Under a causal model in levels with a time-varying effect, the regression residual is a function of the period-one treatment $D_{1}$. Then, researchers should test if $ΔD$ and $D_{1}$ are correlated: if they are, the regression may suffer from an omitted variable bias. To solve it, researchers may control nonparametrically for $E(ΔD|D_{1})$. We use our results to revisit first-difference regressions estimated on the data of \cite{acemoglu2016import}, who study the effect of imports from China on US employment. $ΔD$ and $D_{1}$ are strongly correlated, thus implying that first-difference regressions may be biased if the effect of Chinese imports changes over time. The coefficient on $ΔD$ is no longer significant when controlling for $E(ΔD|D_{1})$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_03208 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Randomly Assigned First Differences? Argañaraz, Facundo de Chaisemartin, Clément Lei, Ziteng Econometrics We consider treatment-effect estimation using a first-difference regression of an outcome evolution $ΔY$ on a treatment evolution $ΔD$. Under a causal model in levels with a time-varying effect, the regression residual is a function of the period-one treatment $D_{1}$. Then, researchers should test if $ΔD$ and $D_{1}$ are correlated: if they are, the regression may suffer from an omitted variable bias. To solve it, researchers may control nonparametrically for $E(ΔD|D_{1})$. We use our results to revisit first-difference regressions estimated on the data of \cite{acemoglu2016import}, who study the effect of imports from China on US employment. $ΔD$ and $D_{1}$ are strongly correlated, thus implying that first-difference regressions may be biased if the effect of Chinese imports changes over time. The coefficient on $ΔD$ is no longer significant when controlling for $E(ΔD|D_{1})$. |
| title | Randomly Assigned First Differences? |
| topic | Econometrics |
| url | https://arxiv.org/abs/2411.03208 |