Hello everyone,

I use a stacked first differences model to estimate the impact of globalization on the relative unemployment rate of unskilled labor in Western Europe.
I have a panel dataset with 16 countries observed at four different times. The estimated model is of the following form:
∆yit = β1∆xit + Ct-1 + vt + eit
∆yit = change in the relative unemployment rate (unskilled vs. skilled) in country i from time t-1 to t
∆xit = change in Chinese import exposure per worker in country i from time t-1 to t
C: a vector of control variables at the start of each period
vt: time dummy for each period

My understanding is that using such a stacked first difference model eliminates unobserved time-invariant variables that vary across countries. Hence, I don't have to include country-specific fixed effects.
How do I control for unobserved variables that are constant across countries but vary over time in such a model? Can one include time fixed effects in a first differences model?

Thank you for your help!