Randomly Assigned First Differences?

Abstract

We consider treatment-effect estimation using a first-difference regression of an outcome evolution Y on a treatment evolution 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 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( 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 acemoglu2016import. D and D_1 are strongly correlated. Controlling for E( D|D_1) halves the estimated effect of Chinese imports.

Tasks

Reproductions