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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:

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My question is why should I include "undifferenced" controls (Xit) in the first difference model?

Thank you in advance for any answers!

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You are allowed to mix differenced and undifferenced variables. Just because dependent variable is differenced does not mean all variables have to be.

Typically you difference variables because:

  • level variables have unit root
  • you actually want to study differenced variables

However, if a variable is stationary and you are interested in an effect of the variable on dependent variable then there is no reason to include it in first differences.

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