I am currently reading the Paper of Dippel et al. (2015), where the authors estimate the causal effect of imports on voting behavior in Germany. Therefore, they estimate the following first-difference specification, where Yit refers to electoral outcomes, NetExposure refers to import - export exposure, τtr are time-varying fixed effects and Xit is a of control variables:
My question is why should I include "undifferenced" controls (Xit) in the first difference model?
Thank you in advance for any answers!