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I'm working on a panel with N=4 and T=76, trying to run the following model:

yt = yt-1 + Xt + controls

where x is an exogenous regressor.

I have two questions:

1)I detected a unit root issue in yt, which is solved differencing. Does it still make sense to include yt-1 as a regressor?

2)I have tried hard to identify the right model to use, but I'm still confused. I have discarded Arellano/Bond-style GMM because they are designed for situations with small T, large N panels. I was considering simple fixed effects model, since stationarity has been taken care of and T is large. Do you have any suggestion?

I would really appreciate your help on this. Many thanks!

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