Randomly Assigned First Differences?

2024-11-05

AI Summary

This paper identifies an implicit endogeneity problem in first-differencing for causal inference: when the initial treatment value $D_1$ is correlated with its first difference $Delta D$, conventional regression of $Delta Y$ on $Delta D$ suffers omitted-variable bias due to uncontrolled variation driven by $D_1$. To address this, we propose controlling for the conditional expectation $E(Delta D mid D_1)$, and prove theoretically that this adjustment consistently eliminates bias arising from initial-value dependence. This is the first systematic identification and mitigation of the $D_1$-dependence structure previously overlooked in first-differencing. Empirical application to industry-level trade shock data from Acemoglu et al. (2016) reveals strong correlation between $Delta D$ and $D_1$. Incorporating our control reduces the estimated effect of U.S. import exposure from China on U.S. industry employment by approximately 50%, substantially improving causal identification reliability.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Knowledge Representation and Reasoning: Action, Change, and Causality

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Trust and reliance of crowd workers and data experts on GenAI
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

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.

Problem

• Address omitted variable bias in first-difference regressions
• Test correlation between treatment evolution and initial treatment
• Re-evaluate biased estimates in Chinese imports' employment impact

Innovation

• Uses first-difference regression for treatment-effect estimation
• Controls nonparametrically for E(ΔD|D₁) to avoid bias
• Revisits biased regressions by testing ΔD and D₁ correlation